List of top Physics Questions on simple harmonic motion

In simple harmonic motion (SHM), the acceleration of a particle at a displacement of 3m from the mean position is $48\text{ m/s}^2$ directed towards the mean position. Find the angular frequency.

A particle performs SHM with an amplitude of 5 cm. Find its acceleration when it is 3 cm from the mean position (assume $ \omega = 2 \, \text{rad/s} $).

The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If the length of the spring is cut to half, the same mass oscillates with frequency $v_2$. The value of $\frac{v_2}{v_1}$ is ________.

A spring stretches by $2\,\text{mm}$ when it is loaded with a mass of $200\,\text{g}$. From equilibrium position the mass is further pulled down by $2\,\text{mm}$ and released. The frequency associated with the system and the maximum energy in the spring are _____ Hz and _____ J, respectively. (Take $g=10\,\text{m/s}^2$).

The equation of motion of a particle is given by $ x = a \sin \left( 50t + \frac{\pi}{3} \right) \, \text{cm}. $ The particle will come to rest at time $ t_1 $ and it will have zero acceleration at time $ t_2 $. The $ t_1 $ and $ t_2 $ respectively are _______.

The velocity of a particle executing simple harmonic motion along x-axis is described as $v^2 = 50 - x^2$, where $x$ represents displacement. If the time period of motion is $\pi/7$ s, the value of $x$ is ______.

A particle is moving along the $x$-axis where the speed varies as \[ v^2 = 100 - x^2 \] Determine the time period.

Position of a particle is given by $ x = A \sin \left( 50t + \frac{\pi}{3} \right) $. If speed and acceleration become 0 for the first time at $ t_1 $ and $ t_2 $ sec respectively, then find $ t_1 $ and $ t_2 $ (in sec):

A 1.5 kg block is placed on a frictionless surface and attached to a spring with a spring constant of 100 N/m. If the block is displaced by 0.2 m from its equilibrium position, what is the potential energy stored in the spring?

A simple pendulum performing small oscillations at a height R above Earth's surface has a time period of $T_1 = 4$ s. What would be its time period at a point which is at a height $2R$ from Earth's surface?

When blue light is incident on metal surface, photoelectrons are emitted. When green light is incident, no photoelectrons are emitted. What is the number of photoelectrons emitted when yellow light is incident?

A simple pendulum of length 1 m is oscillating with a small amplitude. If the acceleration due to gravity is $ 9.8 \, \text{m/s}^2 $, what is the time period of the pendulum?

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Knowing initial position $ x_0 $, and initial momentum $ p_0 $ is enough to determine the position and momentum at any time $ t $ for a simple harmonic motion with a given angular frequency $ \omega $.
Reason (R): The amplitude and phase can be expressed in terms of $ x_0 $ and $ p_0 $.
In the light of the above statements, choose the correct answer from the options given below:

A particle is subjected to simple harmonic motions as: $ x_1 = \sqrt{7} \sin 5t \, \text{cm} $ $ x_2 = 2 \sqrt{7} \sin \left( 5t + \frac{\pi}{3} \right) \, \text{cm} $ where $ x $ is displacement and $ t $ is time in seconds. The maximum acceleration of the particle is $ x \times 10^{-2} \, \text{m/s}^2 $. The value of $ x $ is:

The ratio of the average value of kinetic energy to that of potential energy for an SHM is:

Two simple pendulums having lengths $l_{1}$ and $l_{2}$ with negligible string mass undergo angular displacements $\theta_{1}$ and $\theta_{2}$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

A particle is executing simple harmonic motion with a time period of 2 s and amplitude 1 cm. If $ D $ and $ d $ are the total distance and displacement covered by the particle in 12.5 s, then the ratio $ \frac{D}{d} $ is:

At 27Â°C temperature, the mean kinetic energy of the atoms of an ideal gas is $ E_1 $. If the temperature is increased to 327Â°C, then the mean kinetic energy of the atoms will be

The variation of displacement with time of a simple harmonic motion (SHM) for a particle of mass $ m $ is represented by: \[ y = 2 \sin \left( \frac{\pi}{2} + \phi \right) \, \text{cm} \] The maximum acceleration of the particle is:

T² vs l graph represents:

What is the time taken by a particle executing SHM with a time period $ T $ sec from a positive extreme position to half of the amplitude?

A particle executes SHM with amplitude $ A $ and time period $ T $. The time taken to move from equilibrium to $ \frac{A}{2} $ is:

A particle is executing simple harmonic motion along the $x - axis$, with amplitude $A$, about the origin. Then the ratio of Kinetic energy and total energy at $x = \frac{A}{3}$ is

The potential energy of a particle performing linear S.H.M is $ 0.1 \pi^2 x^2 $ joules. If the mass of the particle is $ 20 \, \mathrm{g} $, find the frequency of S.H.M:

The instantaneous displacement of a particle executing simple harmonic motion is given by $x = 2(\cos(\pi t) + \sin(\pi t))$.
The amplitude of oscillation is