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Simple Harmonic Motion Physics - Simple Harmonic Motion

Rajasthan Board (RBSE) - STD 12 Science - Physics (Rajasthan - English Medium). 110 questions in this chapter.

Question types

Simple Harmonic Motion question types

110 questions across 6 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

110
Questions
6
Question groups
5
Question types
Sample Questions

Simple Harmonic Motion questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
A particle moves in the X - Y plane according to the equation $\overrightarrow{\text{r}}=\Big(\overrightarrow{\text{i}}+2\overrightarrow{\text{j}}\Big)\text{A}\cos\omega\text{t}.$ The motion of the particle is:
  1. On a straight line.
  2. On an ellipse.
  3. Periodic.
  4. Simple harmonic.
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Q 2M.C.Q (1 Marks)1 Mark
A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is $T$. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will:
  • A
    Remain $T$
  • B
    Become $2T$
  • C
    Become $\frac{\text{T}}{2}$
  • ✓
    Become $\frac{\text{T}}{\sqrt{2}}$

Answer: D.

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Q 3M.C.Q (1 Marks)1 Mark
The displacement of a particle is given by $\overrightarrow{\text{r}}=\text{A}\big(\overrightarrow{\text{i}}\cos\omega\text{t}+\overrightarrow{\text{j}}\sin\omega\text{t}\big)$ The motion of the particle is$:$
  • A
    Simple harmonic.
  • B
    On a straight line.
  • ✓
    On a circle.
  • D
    With constant acceleration.

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark
Two bodies $A$ and $B$ of equal mass are suspended from two separate massless springs of spring constant $k_1$ and $k_2$ respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of $A$ to that of $B$ is:
  • A
    $\frac{\text{k}_1}{\text{k}_2}$
  • B
    $\sqrt{\frac{\text{k}_1}{\text{k}_2}}$
  • C
    $\frac{\text{k}_2}{\text{k}_1}$
  • ✓
    $\sqrt{\frac{\text{k}_2}{\text{k}^1}}$

Answer: D.

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Q 61 Marks Question1 Mark
A particle executing simple harmonic motion comes to rest at the extreme positions. Is the resultant force on the particle zero at these positions according to Newton's first law?
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Q 71 Marks Question1 Mark
A platoon of soldiers marches on a road in steps according to the sound of a marching band. The band is stopped and the soldiers are ordered to break the steps while crossing a bridge. Why?
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Q 81 Marks Question1 Mark
The energy of a system in simple harmonic motion is given by $\text{E}=\frac{1}{2}\text{m }\omega^2\text{A}^2.$ Which of the following two statements is more appropriate?
  1. The energy is increased because the amplitude is increased.
  2. The amplitude is increased because the energy is increased.
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Q 101 Marks Question1 Mark
Can simple harmonic motion take place in a noninertial frame? If yes, should the ratio of the force applied with the displacement be constant?
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Q 112 Marks Questions2 Marks
A pendulum having time period equal to two seconds is called a seconds pendulum. Those used in pendulum clocks are of this type. Find, the length of a seconds pendulum at a place where $\text{g}=\pi^2\text{m/s}^2.$
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Q 122 Marks Questions2 Marks
It is proposed to move a particle in simple harmonic motion on a rough horizontal surface by applying an external force along the line of motion. Sketch the graph of the applied force against the position of the particle. Note that the applied force has two values for a given position depending on whether the particle is moving in positive or negative direction.
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Q 132 Marks Questions2 Marks
The angle made by the string of a simple pendulum with the vertical depends on time as $\theta=\frac{\pi}{90}\sin[(\pi\text{s}^{-1})\text{t}].$ Find the length of the pendulum if $\text{g}=\pi^2\text{m/s}^2.$
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Q 142 Marks Questions2 Marks
A pendulum clock giving correct time at a place where $g = 9.800\ m/s^2$ is taken to another place where it loses $24$ seconds during $24$ hours. Find the value of $g$ at this new place.
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Q 152 Marks Questions2 Marks
A simple pendulum of length 40cm is taken inside a deep mine. Assume for the time being that the mine is 1600km deep. Calculate the time period of the pendulum there. Radius of the earth = 6400km.
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Q 163 Marks Question3 Marks
The spring shown in figure is unstretched when a man starts pulling on the cord. The mass of the block is M. If the man exerts a constant force F, find
  1. The amplitude and the time period of the motion of the block,
  2. The energy stored in the spring when the block passes through the equilibrium position and,
  3. The kinetic energy of the block at this position.
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Q 173 Marks Question3 Marks
A simple pendulum of lerigth $1$ feet suspended from the ceiling of an elevator takes $\frac{\pi}{3}$ seconds to complete one oscillation. Find the acceleration of the elevator.
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Q 183 Marks Question3 Marks
A particle is subjected to two simple harmonic motions, one along the X-axis and the other on a line making an angle of 45° with the X-axis, The two motions are given by,$\text{x}=\text{x}_0\sin\omega\text{t}$ and $\text{s}=\text{s}_0\sin\omega\text{t}$
Find the amplitude of the resultant motion.
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Q 193 Marks Question3 Marks
Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude.
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Q 203 Marks Question3 Marks
A body of mass 2kg suspended through a vertical spring executes simple harmonic motion of period 4s. If the oscillations are stopped and the body hangs in equilibrium, find the potential energy stored in the spring.
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Q 214 Marks Questions4 Marks
The ear-ring of a lady shown in has a 3cm long light suspension wire.
  1. Find the time period of small oscillations if the lady is standing on the ground.
  2. The lady now sits in a merry-go-round moving at 4m/s in a circle of radius 2m. Find the time period of small oscillations of the ear-ring.
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Q 234 Marks Questions4 Marks
A simple pendulum fixed in a car has a time period of $4$ seconds when the car is moving uniformly on a horizontal road. When the accelerator is pressed, the time period changes to $3.99$ seconds. Making an approximate analysis, find the acceleration of the car.
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Q 244 Marks Questions4 Marks
A simple pendulum of length I is suspended from the ceiling of a car moving with a speed v on a circular horizontal road of radius r.
  1. Find the tension in the string when it is at rest with respect to the car.
  2. Find the time period of small oscillation.
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Q 255 Marks Questions5 Marks
Consider a particle moving in simple harmonic motion according to the equation $\text{x}=2.0\cos(50\pi\text{t}+\tan^{-1}0.75)$ where $x$ is in centimetre and $t$ in second. The motion is started at $t = 0$.
  1. When does the particle come to rest for the first time?
  2. When does the acceleration have its maximum magnitude for the first time?
  3. When does the particle come to rest for the second time?
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Q 265 Marks Questions5 Marks
A small block of mass m is kept on a bigger block of mass M which is attached to a vertical spring of spring constant k as shown in the figure. The system oscillates vertically.
  1. Find the resultant force on the smaller block when it is displaced through a distance x above its equilibrium position.
  2. Find the normal force on the smaller block at this position. When is this force smallest in magnitude?
  3. What can be the maximum amplitude with which the two blocks may oscillate together?
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Q 275 Marks Questions5 Marks
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance $\frac{\text{R}}{2}$ from the earth's centre where R is the radius of the earth. The wall of the tunnel is frictionless.
  1. Find the gravitational force exerted by the earth on a particle of mass m placed in the tunnel at a distance x from the centre of the tunnel.
  2. Find the component of this force along the tunnel and perpendicular to the tunnel.
  3. Find the normal force exerted by the wall on the particle.
  4. Find the resultant force on the particle.
  5. Show that the motion of the particle in the tunnel is simple harmonic and find the time period.
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Q 285 Marks Questions5 Marks
Find the time period of small oscillations of the following systems.
  1. A metre stick suspended through the $20\ cm$ mark.
  2. A ring of mass in and radius $r$ suspended through a point on its periphery.
  3. A uniform square plate of edge a suspended through a corner.
  4. A unifrom disc of mass $m$ and radius $r$ suspended through a point $\frac{\text{r}}{2}$ away from the centre.
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