Simple Harmonic Motion

The displacement of a particle performing S.H.M. is given by \(x=5 \sin (3 t+3)\), where \(x\) is in \(\mathrm{cm}\) and \(t\) is in second. The maximum acceleration of the particle will be

A particle excuting S.H.M starts from the mean position. Its amplitude is 'A' and time period '\(\mathrm{T}\)' At what displacement its speed is one-fourth of the maximum speed?

A body is performing S.H.M. of amplitude 'A'. The displacement of the body from a point where kinetic energy is maximum to a point where potential energy is maximum, is

A particle performing S.H.M. when displacement is '\(x\)', the potential energy and restoring force acting on it are denoted by '\(E\)' and '\(F\)' respectively. The relation between \(x, E\) and \(F\) is

An object executes SHM along \(x\)-axis with amplitude \(0.06 \mathrm{~m}\). At certain distance '\(\mathrm{x}\)' metre from mean position, it has kinetic energy \(10 \mathrm{~J}\) and potential energy \(8 \mathrm{~J}\). the distance '$$\ma...

A body executes SHM under the action of force '\(\mathrm{F}_1\)' with time period '\(\mathrm{T}_1\)'. If the force is changed to '\(\mathrm{F_2}\)', it executes SHM with period '\(\mathrm{T_2}\)'. If both the forces '\(\mathrm{F_1}\)' and '...

A bob of simple pendulum of mass 'm' perform \(\mathrm{SHM}\) with amplitude '\(\mathrm{A}\)' and period 'T'. Kinetic energy of pendulum of displacement \(x=\frac{A}{2}\) will be

If the amplitude of linear S.H.M. is decreased then

A mass \(0.4 \mathrm{~kg}\) performs S.H.M. with a frequency \(\frac{16}{\pi} \mathrm{Hz}\). At a certain displacement it has kinetic energy \(2 \mathrm{~J}\) and potential energy \(1.2 \mathrm{~J}\). The amplitude of oscillation is

'\(n\)' waves are produced on a string in 1 second. When the radius of the string is doubled, keeping tension same, the number of waves produced in 1 second for the same harmonic will be

A particle connected to the end of a spring executes S.H.M. with period '\(T_1\)'. While the corresponding period for another spring is '\(\mathrm{T}_2\)'. If the period of oscillation with two springs in series is 'T', then

A body of mass '\(m\)' performs linear S.H.M. given by equation \(x=P \sin \omega t+Q \sin \left(\omega t+\frac{\pi}{2}\right)\). The total energy of the particle at any instant is

A particle is performing S.H.M. with maximum velocity '\(v\)'. If the amplitude is tripled and periodic time is doubled then maximum velocity will be

A pendulum clock is running fast. To correct its time, we should

A child is sitting on a swing which performs S.H.M. It has minimum and maximum heights from ground \(0.75 \mathrm{~cm}\) and \(2 \mathrm{~m}\) respectively. Its maximum speed will be $$\left[\mathrm{g}=10 \frac{\mathrm{m}}{\mathrm{s}^2}\rig...

A particle of mass 5kg is executing S.H.M. with an amplitude 0.3 m and time period \(\frac{\pi}{5}\)s. The maximum value of the force acting on the particle is

Two particles \(\mathrm{P}\) and \(\mathrm{Q}\) performs S.H.M. of same amplitude and frequency along the same straight line. At a particular instant, maximum distance between two particles is \(\sqrt{2}\) a. The initial phase difference be...

A mass '\(\mathrm{m}_1\)' is suspended from a spring of negligible mass. A spring is pulled slightly in downward direction and released, mass performs S.H.M. of period '\(\mathrm{T}_1\)'. If the mass is increased by '\(\mathrm{m}_2\)', the ...

A body performs S.H.M. under the action of force '\(\mathrm{F}_1\)' with period '\(\mathrm{T}_1\)' second. If the force is changed to '\(\mathrm{F}_2\)' it performs S.H.M. with period '\(\mathrm{T_2}\)' second. If both forces '$$\mathrm{F_1...

A particle is suspended from a vertical spring which is executing S.H.M. of frequency \(5 \mathrm{~Hz}\). The spring is unstretched at the highest point of oscillation. Maximum speed of the particle is $$(\mathrm{g} =10 \mathrm{~m} / \mathr...

A particle executes S.H.M. of period \(\frac{2 \pi}{\sqrt{3}}\) second along a straight line \(4 \mathrm{~cm}\) long. The displacement of the particle at which the velocity is numerically equal to the acceleration is

A bob of a simple pendulum has mass $m$ and is oscillating with an amplitude $a$. If the length of the pendulum is $L$, then the maximum tension in the string is $\left[\cos 0^{\circ}=1\right.$, $g=$ acceleration due to gravity]

A body of mass 64 g is made to oscillate turn by turn on two different springs $A$ and $B$. Spring $A$ and $B$ has force constant $4 \frac{\mathrm{~N}}{\mathrm{~m}}$ and $16 \frac{\mathrm{~N}}{\mathrm{~m}}$ respectively. If $T_1$ and $T_2$ ...

Two bodies $A$ and $B$ of equal mass are suspended from two separate massles springs of force constant $k_1$ and $k_2$, respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes ...

For a particle performing SHM when displacement is \(x\), the potential energy and restoring force acting on it is denoted by \(E\) and \(F\), respectively. The relation between \(x, E\) and \(F\) is

A simple pendulum of length \(L\) has mass \(m\) and it oscillates freely with amplitude \(A\). At extreme position, its potential energy is (\(g=\) acceleration due to gravity)

A simple pendulum of length \(I\) has a bob of mass \(m\). It executes SHM of small amplitude A. The maximum tension in the string is (\(g=\) acceleration due to gravity)

A block of mass \(m\) attached to one end of the vertical spring produces extension \(x\). If the block is pulled and released, the periodic time of oscillation is

The damping force of an oscillator is directly proportional to the velocity. The unit of constant of proportionality is

A particle performs simple harmonic motion with period of 3 s . The time taken by it to cover a distance equal to half the amplitude from mean position is [\(\sin 30^{\circ}=0.5\)]

The total energy of a simple harmonic oscillaior is proportional to

In damped SHM, the SI unit of damping constant is

A person measures a time period of a simple pendulum inside a stationary lift and finds it to be $T$. If the lift starts accelerating upwards with an acceleration $\left(\frac{g}{3}\right)$, the time period of the pendulum will be

A particle executes the simple harmonic motion with an amplitude ' $A$ '. The distance travelled by it in one periodic time is

The quantity which does not vary periodically for a particle performing SHM is

If ' $x$ ', $v$ ' and ' $a$ ' denote the displacement, velocity and acceleration of a particle respectively executing SHM of periodic time $h$ then which one of the following does not change with time?

Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulums is

A particle is performing a linear simple harmonic motion of amplitude ' $A$ '. When it is midway between its mean and extreme position, the magnitudes of its velocity and acceleration are equal. What is the periodic time of the motion?