Question 11 Mark
Which of the following examples represent periodic motion? An arrow released from a bow.
Answer
View full question & answer→There is no repetition, hence not periodic.
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Question 21 Mark
Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant): $\text{exp}(-\omega^2\text{t}^2)$
Answer
View full question & answer→Non-periodic motion The given function $\text{exp}(-\omega^2\text{t}^2)$ is an exponential function. Exponential functions do not repeat themselves. Therefore, it is a non-periodic motion.
Question 31 Mark
Which of the following examples represent periodic motion? A swimmer completing one (return) trip from one bank of a river to the other and back.
Answer
View full question & answer→There is no repetition of the motion as the swimmer just completes one trip hence not periodic.
Question 41 Mark
Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?General vibrations of a polyatomic molecule about its equilibrium position.
Answer
View full question & answer→A polyatomic molecule has many natural frequencies of oscillation. Its vibration is the superposition of individual simple harmonic motions of a number of different molecules. Hence, it is not simple harmonic, but periodic.
Question 51 Mark
Fig. depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?
Answer
View full question & answer→In this case, the motion of the particle repeats itself after 2s. Hence, it is a periodic motion, having a period of 2s.
Question 61 Mark
A particle is in linear simple harmonic motion between two points, A and B, 10cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is: At the end A.
Answer
From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.
At the end A, the particle executing SHM is momentarily at rest being its extreme position of motion. Therefore, its velocity is zero. Acceleration is positive because it is directed along AP, Force is also Positive since the force is directed along AP.
View full question & answer→From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.At the end A, the particle executing SHM is momentarily at rest being its extreme position of motion. Therefore, its velocity is zero. Acceleration is positive because it is directed along AP, Force is also Positive since the force is directed along AP.
Question 71 Mark
Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant): $1+\omega\text{t}+\omega^2\text{t}^2$
Answer
View full question & answer→The given function $1+\omega\text{t}+\omega^2\text{t}^2$ is non-periodic.
Question 81 Mark
Which of the following examples represent periodic motion? A freely suspended bar magnet displaced from its N-S direction and released.
Answer
View full question & answer→ The motion is repeated after a certain interval of time, hence periodic. In fact, the bar magnet oscillates about its mean position with a definite period of time.
Question 91 Mark
A particle is in linear simple harmonic motion between two points, A and B, 10cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is:At the mid-point of AB going towards A.
Answer
From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.
At the mid-point of AB going towards A, the particle is at its mean position P, with a tendency to move along PA. Hence, velocity is positive. Both acceleration and force are zero.
View full question & answer→From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.At the mid-point of AB going towards A, the particle is at its mean position P, with a tendency to move along PA. Hence, velocity is positive. Both acceleration and force are zero.
Question 101 Mark
Fig. depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?
Answer
View full question & answer→ It is not a periodic motion. This is because the particle repeats the motion in one position only. For a periodic motion, the entire motion of the particle must be repeated in equal intervals of time.
Question 111 Mark
Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? The rotation of earth about its axis.
Answer
View full question & answer→It is periodic but not simple harmonic motion because it is not to and fro about a fixed point.
Question 121 Mark
A particle is in linear simple harmonic motion between two points, A and B, 10cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is: At the end B.
Answer
From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.
At the end B, velocity is zero. Here, acceleration and force are negative as they are directed along BP.
View full question & answer→From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.At the end B, velocity is zero. Here, acceleration and force are negative as they are directed along BP.
Question 131 Mark
A particle is in linear simple harmonic motion between two points, A and B, 10cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is:At 3cm away from A going towards B.
Answer
From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.
At 3cm away from A going towards B, the particle is at R, with a tendency to move along RP, which is positive direction. Here, velocity, acceleration all are positive.
View full question & answer→From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.At 3cm away from A going towards B, the particle is at R, with a tendency to move along RP, which is positive direction. Here, velocity, acceleration all are positive.
MCQ 141 Mark
Which of the following relationships between the acceleration a and the displacement $x$ of a particle involve simple harmonic motion?
- A$a=0.7 x$
- B$a=-200 x^2$
- ✓$a=-10 x$
- D$a=100 x^3$
Answer
View full question & answer→Correct option: C.
$a=-10 x$
In $\text{SHM}$, acceleration a is related to displacement by the relation of the form $a = -kx$, which is for relation $(c)$.
Question 151 Mark
Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower most point.
Answer
View full question & answer→It is simple harmonic motion because the ball moves to and fro about the lowermost point of the bowl when released. Also, the ball comes back to its initial position in the same period of time, again and again.
Question 161 Mark
Which of the following examples represent periodic motion?A hydrogen molecule rotating about its centre of mass.
Answer
View full question & answer→ Rotatary motion is periodic as repeating after fixed time-interval.
Question 171 Mark
A particle is in linear simple harmonic motion between two points, A and B, 10cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is:At 2cm away from B going towards A.
Answer
From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.
At 2cm away from B going towards A, the particle is at Q, with a tendency to move along QP, which is negative direction. Therefore, velocity, acceleration and force all are positive.
View full question & answer→From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.At 2cm away from B going towards A, the particle is at Q, with a tendency to move along QP, which is negative direction. Therefore, velocity, acceleration and force all are positive.
Question 181 Mark
A particle is in linear simple harmonic motion between two points, A and B, 10cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is:At 4cm away from B going towards A.
Answer
From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.
At 4cm away from A going towards A, the particles is at S, with a tendency to move along SA, which is negative direction. Therefore, velocity is negative but acceleration is directed towards mean position, along SP. Hence it is positive and also force is positive similarly.
View full question & answer→From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.At 4cm away from A going towards A, the particles is at S, with a tendency to move along SA, which is negative direction. Therefore, velocity is negative but acceleration is directed towards mean position, along SP. Hence it is positive and also force is positive similarly.
Question 191 Mark
Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? Motion of an oscillating mercury column in a U-tube.
Answer
View full question & answer→It is a simple harmonic motion because the mercury moves to and fro on the same path, about the fixed position, with a certain period of time.
Question 201 Mark
Figure (a) shows a spring of force constant k clamped rigidly at one end and a mass m attached to its free end. A force F applied at the free end stretches the spring. Figure (b) shows the same spring with both ends free and attached to a mass m at either end. Each end of the spring in Fig. (b) is stretched by the same force F.
What is the maximum extension of the spring in the two cases?
What is the maximum extension of the spring in the two cases?
Answer
View full question & answer→The maximum extension of the spring in both cases will = Flk, where k is the spring constant of the springs used.
Question 211 Mark
Fig. depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?
Answer
View full question & answer→ In this case, the motion of the particle repeats itself after 2s. Hence, it is a periodic motion, having a period of 2s.
Question 221 Mark
Fig. depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?
Answer
View full question & answer→It is not a periodic motion. This represents a unidirectional, linear uniform motion. There is no repetition of motion in this case.
Question 231 Mark
Answer the following questions:What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?
Answer
View full question & answer→ When a simple pendulum mounted in a cabin falls freely under gravity, its acceleration is zero. Hence the frequency of oscillation of this simple pendulum is zero.
Question 241 Mark
Which of the following examples represent periodic motion? An arrow released from a bow.
Answer
View full question & answer→There is no repetition, hence not periodic.
Question 251 Mark
How is the path difference related to phase difference?
Answer
View full question & answer→ Path difference $=\frac{\lambda}{2\pi}\times\text{phase difference}$
Question 261 Mark
Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant):$\text{exp}(-\omega^2\text{t}^2)$
Answer
View full question & answer→Non-periodic motion The given function $\text{exp}(-\omega^2\text{t}^2)$ is an exponential function. Exponential functions do not repeat themselves. Therefore, it is a non-periodic motion.
Question 271 Mark
What is an epoch? Name the unit in which it is measured.
Answer
View full question & answer→ The initial difference in position from mean position expressed in radians is called epoch.
Question 281 Mark
What is the force equation of a SHM?
Answer
View full question & answer→According to force equation of SHM, F = -kx, where, k is a constant known as force constant.
Question 291 Mark
A body of mass m is situated in a potential field $\text{U}(\text{x})=\text{U}_0(1-\cos\text{ax}),$ Where $U_0$ and a are constant. find the time period of small oscillation.
Answer
View full question & answer→$\because\text{dW}=\text{F}.\text{dx}$ if W = U, then$\text{dU}=\text{F}.\text{dx}\ \text{or}\ \text{F}=\frac{-\text{dU}}{\text{dx}}$ (here restoring force is opposite to displacement)
$\text{F}=\frac{-\text{d}}{\text{dx}}[\text{U}_0(1-\cos\text{ax})=\frac{-\text{d}}{\text{dx}}[\text{U}_0+\text{U}_0\cos\text{a}_\text{x}]$
$\text{F}=-[0-\text{U}_0(-\sin\text{ax}).\text{a}]$
$\text{F}=-\text{aU}_0\sin\text{a}\text{x}$
For SHM. ax is small
So sin ax becomes ax ...(i)
$\therefore\text{F}=-\alpha.\text{U}_0\text{ax}=-\text{a}^2\text{U}_0\text{x}\ ...(\text{ii})$
$\alpha_2\text{U}_0$ are constants.
$\therefore\text{F}\propto-\text{x}.$ so motion is SHM.
Here from (ii) $k = a^2U_0$
$\text{m}\omega^2=\text{a}^2\text{U}_0\Rightarrow\omega^2=\text{a}^2\frac{\text{U}_0}{\text{m}}$
$\Big(\frac{2\pi}{\text{T}}\Big)^2=\text{a}^2\frac{\text{U}_0}{\text{m}}\Rightarrow\text{T}^2=4\pi\frac{\text{m}}{\text{U}_0\text{a}^2}\ \text{or}$
$\text{T}=\frac{2\pi}{\text{a}}\sqrt{\frac{\text{m}}{\text{U}_0}}.$
From (i) this time period is valid for small angle ax.
$\text{F}=\frac{-\text{d}}{\text{dx}}[\text{U}_0(1-\cos\text{ax})=\frac{-\text{d}}{\text{dx}}[\text{U}_0+\text{U}_0\cos\text{a}_\text{x}]$
$\text{F}=-[0-\text{U}_0(-\sin\text{ax}).\text{a}]$
$\text{F}=-\text{aU}_0\sin\text{a}\text{x}$
For SHM. ax is small
So sin ax becomes ax ...(i)
$\therefore\text{F}=-\alpha.\text{U}_0\text{ax}=-\text{a}^2\text{U}_0\text{x}\ ...(\text{ii})$
$\alpha_2\text{U}_0$ are constants.
$\therefore\text{F}\propto-\text{x}.$ so motion is SHM.
Here from (ii) $k = a^2U_0$
$\text{m}\omega^2=\text{a}^2\text{U}_0\Rightarrow\omega^2=\text{a}^2\frac{\text{U}_0}{\text{m}}$
$\Big(\frac{2\pi}{\text{T}}\Big)^2=\text{a}^2\frac{\text{U}_0}{\text{m}}\Rightarrow\text{T}^2=4\pi\frac{\text{m}}{\text{U}_0\text{a}^2}\ \text{or}$
$\text{T}=\frac{2\pi}{\text{a}}\sqrt{\frac{\text{m}}{\text{U}_0}}.$
From (i) this time period is valid for small angle ax.
Question 301 Mark
What happens to the time period of a simple pendulum if its length is doubled?
Answer
View full question & answer→ The time period is increased by a factor of $\sqrt{2}$.
Question 311 Mark
What forces keep the simple pendulum in simple harmonic motion?
Answer
View full question & answer→ Restoring force $\text{mg}\sin\theta$ and proper tension maintain simple harmonic motion in simple pendulum.
Question 321 Mark
Is the damping force constant on a system executing S.H.M?
Answer
View full question & answer→ No. It is directly proportional to velocity which is a variable with time.
Question 331 Mark
Why a point on a rotating wheel cannot be considered as executing S.H.M.?
Answer
View full question & answer→It is only periodic and not oscillatory.
Question 341 Mark
Which of the following examples represent periodic motion? A swimmer completing one (return) trip from one bank of a river to the other and back.
Answer
View full question & answer→There is no repetition of the motion as the swimmer just completes one trip hence not periodic.
Question 351 Mark
Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?General vibrations of a polyatomic molecule about its equilibrium position.
Answer
View full question & answer→A polyatomic molecule has many natural frequencies of oscillation. Its vibration is the superposition of individual simple harmonic motions of a number of different molecules. Hence, it is not simple harmonic, but periodic.
Question 361 Mark
A pendulum is making one oscillation in every two seconds. What is the frequency of oscillation?
Answer
View full question & answer→0.5Hz.
Question 371 Mark
Why does the time period of a swing not change when two persons sit on it instead of one?
Answer
View full question & answer→ $\text{T}=2\pi\frac{\text{l}}{\text{g}},$ so it does not depend upon the mass.
Question 381 Mark
What will be the time period of oscillation, if the length of a second pendulum is one third?
Answer
View full question & answer→$\frac{\text{T}_2^2}{\text{T}_1^2}=\frac{\text{l}_2}{\text{l}_1}\frac{\Big(\frac{\text{l}}{3}\Big)}{\text{l}}\frac{1}{3}$$\frac{\text{T}_2^2}{\text{T}_1^2}=\frac{(2)^2}{3}$
$\text{T}_2=\frac{2}{\sqrt{3}}\text{s}$
$\text{T}_2=\frac{2}{\sqrt{3}}\text{s}$
Question 391 Mark
What are the basic properties required by a system to oscillate?
Answer
View full question & answer→Inertia and elasticity are the properties which are required by a system to oscillate.
Question 401 Mark
Is it correct to say the “linear combinations of S.H.M. is a S.H.M."?
Answer
View full question & answer→Yes, e.g., $\text{a}\sin\omega\text{t + b}\cos\omega\text{t}$ is a linear combination which is also S.H.M. with amplitude $\sqrt{\text{a}^2+\text{b}^2}.$
Question 411 Mark
What is the main difference between forced oscillations and resonance?
Answer
View full question & answer→In forced oscillations, a body oscillates with the help of external periodic force with a frequency different from natural frequency of body but in resonance a body oscillates with its own natural frequency with the help of an external periodic force whose frequency is equal to natural frequency of body.
Question 421 Mark
Two exactly similar simple pendula are vibrating with amplitudes 1cm and 3cm. What is the ratio of their energies of vibration?
Answer
View full question & answer→$\frac{\text{E}_1}{\text{E}_2}=\frac{\text{a}_1^2}{\text{a}_2^2}=\Big(\frac{1}{3}\Big)^2=\frac{1}{9}$.
Question 431 Mark
Can the motion of an artificial satellite around earth be taken as S.H.M?
Answer
View full question & answer→ No, it is a circular and periodic motion but not to and fro about a mean position which is essential for SHM.
Question 441 Mark
What is the phase difference between particle velocity and particle acceleration in SHM?
Answer
View full question & answer→Particle acceleration in SHM is ahead in phase by $\frac{\pi}{2}$ as compared to the particle velocity.
Question 451 Mark
Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant):$1+\omega\text{t}+\omega^2\text{t}^2$
Answer
View full question & answer→The given function $1+\omega\text{t}+\omega^2\text{t}^2$ is non-periodic.
Question 461 Mark
Two springs of force constants $\text{k}_1$ and $\text{k}_2$ are joined in series. What is the force constant of the combination?
Answer
View full question & answer→The force constant k of series combination is given by $\frac{1}{\text{k}}=\frac{1}{\text{k}_1}+\frac{1}{\text{k}_2}$$\text{k}=\frac{\text{k}_1\text{k}_2}{\text{k}_1+\text{k}_2}$.
Question 471 Mark
Which of the following examples represent periodic motion? A freely suspended bar magnet displaced from its N-S direction and released.
Answer
View full question & answer→The motion is repeated after a certain interval of time, hence periodic. In fact, the bar magnet oscillates about its mean position with a definite period of time.
Question 481 Mark
How would the period of spring mass system change, when it is made to oscillate horizontally and then vertically?
Answer
View full question & answer→The time period remains same in both the cases.
Question 491 Mark
A particle is in linear simple harmonic motion between two points, A and B, 10cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is:At the mid-point of AB going towards A.
Answer
From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.
At the mid-point of AB going towards A, the particle is at its mean position P, with a tendency to move along PA. Hence, velocity is positive. Both acceleration and force are zero.
View full question & answer→From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.At the mid-point of AB going towards A, the particle is at its mean position P, with a tendency to move along PA. Hence, velocity is positive. Both acceleration and force are zero.
Question 501 Mark
When a pendulum clock gains time, what adjustment should be made?
Answer
View full question & answer→When a pendulum clock gains time, it means it has gone fast i.e., it makes more vibrations per day than required. This shows that the time period of oscillation has decreased. Therefore, to correct it, the length of pendulum should be properly increased.