The total mechanical energy of a linear harmonic oscillator is 600 J. At the mean position its potential energy is 100 J. The minimum potential energy of oscillator is 

A general graph showing variation in potential energy (PE) of a particle with time while executing S.H.M. is

A spring has equilibrium elongation 0.1 m when suspended vertically with a load. If the load is slightly displaced vertically downward and released, then the time period of SHM of the system will be approximately

Select the correct statement regarding potential energy (U) in the simple harmonic motion of a particle along x-axis.

A simple pendulum is pushed slightly from its equilibrium towards left and then set free to execute S.H.M. Select correct graph between its velocity(V) and displacement (x).

Simple harmonic motion is an example of

A particle under SHM takes 1.2 s to complete one vibration. Minimum time taken by it to travel from mean position to half of its amplitude is

The potential energy of a particle executing SHM at the extreme position and mean position are 20 J and 5 J respectively. The kinetic energy of the particle at the mean position is:

Equation of simple harmonic motion of a particle is y = (0.4 m) sin314t, where time t is in second. Frequency of vibration of the particle is

A particle starts SHM from the mean position. Its amplitude is A and time period is T. At the time when its speed is half of its maximum speed, its displacement is

The acceleration of a particle in SHM is

A particle moves in the XY plane according to the equation $\overrightarrow{\mathrm{r}} = \left(5\mathrm{i} + 3\mathrm{j}\right) \sin 2\mathrm{t}$. The motion of the particle is along:

A particle is performing SHM with amplitude A and angular velocity $\omega$. The ratio of the magnitude of maximum velocity to maximum acceleration is

The potential energy of a particle executing SHM is 2.5 J when its displacement is half of the amplitude. The total energy of the particle is:

Choose the incorrect statement.

If a simple pendulum is suspended from the roof of a trolley which moves in the horizontal direction with an acceleration a, then the time period is given by $\mathrm{T} = 2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\mathrm{g}\text{'}}}$, where $g\text{'}$ is equal to:

In the given figure, when two identical springs are attached with a body of mass m, then oscillation frequency is f. If one spring is removed, then the frequency will become

The function ${\sin }^2\left(\omega t\right)$ represents:

Values of the acceleration A of a particle moving in simple harmonic motion as a function of its displacement x are given below

$\mathbf{A}\mathbf{ }\mathbf{\left(}\mathbf{mms}{\mathbf{-}}^{\mathbf{2}}\mathbf{\right)}$      16   8   0   8   -16

x  (mm)                  4    -2   0   2     4

The period of the motion is :

The acceleration-time graph of a particle undergoing SHM is shown in the figure.

For a particle executing simple harmonic motion, the kinetic energy is given by $\mathrm{K} = {\mathrm{K}}_0 {\cos }^2\mathrm{\omega t}$. Then the maximum value of potential energy for the given particle : 

A body executes oscillations under the effect of a small damping force. If the amplitude of the body reduces by 50% in 6 minutes, then amplitude after the next 12 minutes will be [initial amplitude is ${\mathrm{A}}_0$] -

A body of mass M is situated in a potential field. The potential energy of the body is given by $\mathrm{U}\left(\mathrm{x}\right) = {\mathrm{U}}_0\left[1 - \cos \mathrm{Kx}\right]$; where x is position, K and ${\mathrm{U}}_0$ are constant. Period of small oscillations of the body will be:

A particle is executing SHM about origin along X-axis, between points A($\alpha$, 0) and B(-$\alpha$, 0). Its time period of oscillation is T. The magnitude of its acceleration $\frac{\mathrm{T}}{12}$ second after the particle reaches point A will be

A particle executes linear oscillation such that its epoch is zero. The ratio of the magnitude of its displacement in 1st second and 2nd second is (Time period = 12 seconds)

A block of mass 0.02 kg is connected with spring and is free to oscillate on a horizontal smooth surface as shown. The angular frequency of oscillation is 2 rad ${\mathrm{s}}^{-1}$. The block is pulled by 4 cm (from equilibrium position) and then pushed towards the spring with a velocity of 8 cm/s. The amplitude of oscillation is (Neglect any damping)

A particle moves on a circular path with uniform speed about the origin. The x-t graph will be (x : value of x-coordinate; t-time)

A simple pendulum has time period T. The bob is given negative charge and surface below it is given a positive charge. The new time period will be

A simple pendulum attached to the ceiling of a stationary lift has a time period of 1 s. The distance y covered by the lift moving downward varies with time as y = 3.75 ${\mathrm{t}}^2$, where y is in meters and t is in seconds. If g = 10 $\mathrm{m}/{\mathrm{s}}^2$, then the time period of the pendulum will be

Which of the following may represent the potential energy of a body in S.H.M.? (Symbols have usual meaning)