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18 questions · self-marked practice — reveal the answer and mark yourself.

Question 11 Mark
The ratio of frequencies of two pendulums are 2 : 3, then their lengths are in ratio of .
Answer
The ratio of frequencies of two pendulums are 2 : 3, then their lengths are in ratio of $\frac{9}{4}.$
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Question 21 Mark
State of particle regarding its position and direction of motion at any instant is known as .
Answer
State of particle regarding its position and direction of motion at any instant is known as phase.
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Question 31 Mark
Time period of a pendulum hanged in a satellite is .
Answer
Time period of a pendulum hanged in a satellite is zero.
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Question 41 Mark
Time period of simple pendulum executing simple harmonic motion is .
Answer
Time period of simple pendulum executing simple harmonic motion is $\text{T}=2\pi\sqrt{\frac{\text{l}}{\text{g}}}.$
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Question 51 Mark
A particle executes simple harmonic motion with a frequency f. The frequency with which its kinetic energy oscillates is .
Answer
A particle executes simple harmonic motion with a frequency f. The frequency with which its kinetic energy oscillates is 2f.
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Question 61 Mark
If a spring has time period T and is cut into n equal parts then the time period of each part will be .
Answer
If a spring has time period T and is cut into n equal parts then the time period of each part will be $\frac{\text{T}}{\sqrt{\text{n}}}.$
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Question 71 Mark
The oscillations in which the amplitude decreases gradually with passage of time are called .
Answer
The oscillations in which the amplitude decreases gradually with passage of time are called damped oscillations​​​​​​​.
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Question 81 Mark
Total energy of particle executing S.H.M. is given $\text{E}=2\pi^2\text{mv}^2\text{A}^2$
Answer
Total energy of particle executing S.H.M. is given ________.
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Question 91 Mark
In body moves back and forth repeatedly about its mean position under influence of restoring force that act toward mean position and proportional to displacement.
Answer
In simple harmonic motion body moves back and forth repeatedly about its mean position under influence of restoring force that act toward mean position and proportional to displacement.
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Question 101 Mark
The displacement y of a particle executing periodic motion is given by$\text{y}=4\cos^2\Big(\frac{\text{t}}{2}\Big)\sin(1000\text{t})$
This expression may be considered to be a result of the superposition of _______ independent harmonics.
Answer
The displacement y of a particle executing periodic motion is given by$\text{y}=4\cos^2\Big(\frac{\text{t}}{2}\Big)\sin(1000\text{t})$
This expression may be considered to be a result of the superposition of Three independent harmonics.Explanation:
$\text{y}=4\cos^2\Big(\frac{\text{t}}{2}\Big)\sin1000\text{t}$
$=2(1+\cos\text{t})\sin1000\text{t}$ $(\because2\cos^2\theta=1+\cos2\theta)$
$=2\sin1000\text{t}+2\sin1000\text{t}\cos\text{t}$
$=2\sin1000\text{t}+\sin(1000+1)\text{t}\\+\sin(1000-1)\text{t}$ $[\because2\sin\text{A}\cos\text{B}=\sin(\text{A + B})+\sin(\text{A}-\text{B})]$
$=2\sin1000\text{t}+\sin1001\text{t}+\sin999\text{t}$
This shows that the given expression is the result of three independent harmonics.
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Question 111 Mark
Acceleration of a particle in simple harmonic motion is .
Answer
Acceleration of a particle in simple harmonic motion is $\text{a}=-\omega^2\text{x}.$
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Question 121 Mark
Velocity of particle executing simple harmonic motion is maximum at mean position while at extreme position .
Answer
Velocity of particle executing simple harmonic motion is maximum at mean position $\text{v(t)}=-\omega\text{A}$ while at extreme position zero.
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Question 131 Mark
Any motion that repeats itself over and over again at regular interval of time is called .
Answer
Any motion that repeats itself over and over again at regular interval of time is called harmonic motion.
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Question 141 Mark
When the maximum K.E. of a simple pendulum is K, then its displacement is when kinetic energy is $\frac{\text{K}}{2}$ and amplitude is a.
Answer
When the maximum K.E. of a simple pendulum is K, then its displacement is $\frac{\text{a}}{\sqrt{2}}$ when kinetic energy is $\frac{\text{K}}{2}$ and amplitude is a.
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Question 151 Mark
Maximum displacement of the oscillating particle on either side of its mean position is called its .
Answer
Maximum displacement of the oscillating particle on either side of its mean position is called its amplitude.
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Question 161 Mark
A child swinging on a swing in sitting position stands up then the time period of the swing will _________.
Answer
A child swinging on a swing in sitting position stands up then the time period of the swing will Decrease.
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Question 171 Mark
When body is oscillating under the influence of external periodic force with frequency equal to natural frequency of body, then amplitude become maximum this condition is known as .
Answer
When body is oscillating under the influence of external periodic force with frequency equal to natural frequency of body, then amplitude become maximum this condition is known as resonance.
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Question 181 Mark
Time period of a body executing simple harmonic motion _______.
Answer
Time period of a body executing simple harmonic motion $\text{T}=2\pi\sqrt{\frac{\text{lnertia factor}}{\text{Spring factor}}}.$
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