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 $\text{g}=\pi^2\text{m/s}^2.$
View full solution →Question types
Simple Harmonic Motion question types
111 questions across 6 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.
111
Questions
6
Question groups
5
Question types
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2 Marks Questions
12 Q→023 Marks Question
20 Q→031 Marks Question
11 Q→044 Marks Questions
4 Q→05M.C.Q (1 Marks)
37 Q→065 Marks Questions
27 Q→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.
A pendulum clock giving correct time at a place where g = 9.800m/s2 is taken to another place where it loses 24 seconds during 24 hours. Find the value of g at this new place.
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.
A particle executes simple harmonic motion with an amplitude of 10cm. At what distance from the mean position are the kinetic and potential energies equal?
A hollow sphere filled with water is used as the bob of a pendulum. Assume that the equation for simple pendulum is valid with the distance between the point of suspension and centre of mass of the bob acting as the effective length of the pendulum. If water slowly leaks out of the bob, how will the time period vary?
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.
View full solution →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,
View full solution →$\text{x}=\text{x}_0\sin\omega\text{t}$ and $\text{s}=\text{s}_0\sin\omega\text{t}$
Find the amplitude of the resultant motion.A particle of mass in is attatched to three springs A, B and C of equal force constants k as shown in figure If the particle is pushed slightly against the spring C and released, find the time period of oscillation.
The string, the spring and the pulley shown in figure are light. Find the time period of the mass m.
A particle is subjected to two simple harmonic motions of same time period in the same direction. The amplitude of the first motion is 3.0cm and that of the second is 4.0cm. Find the resultant amplitude if the phase difference between the motions is:
- 0°
- 60°
- 90°
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?
View full solution →- The energy is increased because the amplitude is increased.
- The amplitude is increased because the energy is increased.
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?
A pendulum clock gives correct time at the equator. Will it gain time or loose time as it is taken to the poles?
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?
Can simple harmonic motion take place in a noninertial frame? If yes, should the ratio of the force applied with the displacement be constant?
A person goes to bed at sharp 10:00 pm every day. Is it an example of periodic motion? If yes, what is the time period? If no, why?
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.
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.
- Find the tension in the string when it is at rest with respect to the car.
- Find the time period of small oscillation.
The ear-ring of a lady shown in has a 3cm long light suspension wire.
- Find the time period of small oscillations if the lady is standing on the ground.
- 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.
A student says that he had applied a force $\text{F}=-\text{k}\sqrt{\text{x}}$ on a particle and the particle moved in simple harmonic motion. He refuses to tell whether k is a constant or not. Assume that he was worked only with positive x and no other force acted on the particle.
View full solution →- As x increases k increases.
- As x increases k decreases.
- As x increases k remains constant.
- The motion cannot be simple harmonic.
Which of the following quantities are always negative in a simple harmonic motion?
View full solution →-
$\overrightarrow{\text{F}}.\overrightarrow{\text{a}}$
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$\overrightarrow{\text{v}}.\overrightarrow{\text{r}}$
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$\overrightarrow{\text{a}}.\overrightarrow{\text{r}}$
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$\overrightarrow{\text{F}}.\overrightarrow{\text{r}}$
Which of the following quantities are always zero in a simple harmonic motion?
View full solution →-
$\overrightarrow{\text{F}}\times\overrightarrow{\text{a}}$
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$\overrightarrow{\text{v}}\times\overrightarrow{\text{r}}$
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$\overrightarrow{\text{a}}\times\overrightarrow{\text{r}}$
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$\overrightarrow{\text{F}}\times\overrightarrow{\text{r}}$
The total mechanical energy of a spring-mass system in 1 simple harmonic motion is $\text{E}=\frac{1}{2}\text{m}\omega^2\text{A}^2.$ Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will:
View full solution →- Become 2E
- Become $\frac{\text{E}}{2}$
- Become $\sqrt{2\text{E}}$
- Remain E.
The average energy in one time period in simple harmonic motion is:
View full solution →-
$\frac{1}{2}\text{m}\omega^2\text{A}^2$
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$\frac{1}{4}\text{m}\omega^2\text{A}^2$
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$\text{m}\omega^2\text{A}^2$
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$\text{Zero}$
Two small balls, each of mass m are connected by a light rigid rod of length L. The system is suspended from its centre by a thin wire of torsional constant k. The rod is rotated about the wire through an angle $\theta_0$ and released. Find the tension in the rod' as the system passes through the mean position.
View full solution →
Assume that a tunnel is dug across the earth (radius = R) passing through its centre. Find the time a particle takes to cover the length of the tunnel if,
View full solution →- It is projected into the tunnel with a speed of $\sqrt{\text{gR}}.$
- It is released from a height R above the tunnel.
- It is thrown vertically upward along the length of tunnel with a speed of $\sqrt{\text{gR}}.$
The block of mass m1 shown in figure is fastened to the spring and the block of mass m2 is placed against it.
View full solution →- Find the compression of the spring in the equilibrium position.
- The blocks are pushed a further distance $\big(\frac{2}{\text{k}}\big)(\text{m}_1+\text{m}_2)\text{g}\sin\theta$ sine against the spring and released. Find the position where the two blocks separate.
- What is the common speed of blocks at the time of separation?
The equation of motion of a particle started at t = 0 is given by $\text{x}=5\sin\big(20\text{t}+\frac{\pi}{3}\big)$ where x is in centimetre and t in second. When does the particle.
View full solution →- First come to rest.
- First have zero acceleration.
- First have maximum speed?
A particle is subjected to two simple harmonic motions given by $\text{x}_1=2.0\sin(100\pi\text{t})$ and $\text{x}_2=2.0\sin\Big(120\pi\text{t}+\frac{\pi}{3}\Big)$ where x is in centimeter and t in second. Find the displacement of the particle at
View full solution →- t = 0.0125.
- t = 0.025.
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