Simple Harmonic Motion

The bob of a pendulum of length ' $l$ ' is pulled aside from its equilibrium position through an angle ' $\theta$ ' and then released. The bob will then pass through its equilibrium position with speed ' $v$ ', where ' $v$ ' equal to ( $g=$...

A particle performs linear S.H.M. At a particular instant, velocity of the particle is ' $u$ ' and acceleration is ' $\alpha$ ' while at another instant, velocity is ' $v$ ' and acceleration is ' $\beta$ ' $(0<\alpha<\beta)$. The distance b...

The kinetic energy of a particle, executing simple harmonic motion is 16 J when it is in mean position. If amplitude of motion is 25 cm and the mass of the particle is 5.12 kg , the period of oscillation is

A horizontal platform with a small object placed on it executes a linear S.H.M. in the vertical direction. The amplitude of oscillation is 40 cm . What should be the least period of these oscillations, so that the object is not detached fro...

The maximum velocity of a particle, executing S.H.M. with an amplitude 7 mm is $4.4 \mathrm{~ms}^{-1}$

The period of oscillation is $\left[\pi=\frac{22}{7}\right]$

Starting from mean position, a body oscillates simple harmonically with a period ' $T$ '. After what time will its kinetic energy be $75 \%$ of the total energy? $\left(\sin 30^{\circ}=0.5\right)$

For a particle executing S.H.M. having amplitude A, the speed of the article is $\left(\frac{1}{3}\right)^{\text {rd }}$ of its maximum speed when the displacement from the mean position is

The motion of a particle is described by the equation $a=-b x$ where ' $a$ ' is the acceleration, x is the displacement from the equilibrium position and b is a constant. The periodic time will be

A particle performs linear S.H.M. at a particular instant, velocity of the particle is ' $u$ ' and acceleration is ' $\mathrm{a}_1$ ' while at another instant velocity is ' V ' and acceleration is ' $a_2$ ' $\left(0

A simple pendulum of length ' $L$ ' has mass ' $M$ ' and it oscillates freely with amplitude ' $A$ '. At extreme position, its potential energy is

A particle performing S.H.M. starts from equilibrium position and its time period is 12 second. After 2 seconds its velocity is $\pi \mathrm{m} / \mathrm{s}$. Amplitude of the oscillation is $\left[\sin 30^{\circ}=\cos 60^{\circ}=0 \cdot 5,...

All the springs in fig. (a), (b) and (c) are identical, each having force constant K . Mass attached to each system is ' $m$ '. If $T_a, T_b$ and $T_c$ are the time periods of oscillations of the three systems respectively, then

A piece of wood has length, breadth and height, ' $a$ ', ' $b$ ' and ' $c$ ' respectively. Its relative density, is ' $d$ '. It is floating in water such that the side ' $a$ ' is vertical. It is pushed down a little and released. The time p...

A particle is performing S.H.M. about its mean position with an amplitude ' $a$ ' and periodic time ' $T$ '. The speed of the particle when its displacement from mean position is $\frac{a}{3}$ will be

A particle performing S.H.M. with maximum velocity ' $V$ '. If the amplitude double and periodic time is made, $\left(\frac{1}{3}\right)^{\text {rd }}$ then the maximum velocity is

Let ' $l_1$ ' be the length of simple pendulum. Its length changes to ' $l_2$ ' to increase the periodic time by $20 \%$. The ratio $\frac{l_2}{l_1}=$

A particle performs linear S.H.M. When the displacement of the particle from mean position is 3 cm and 4 cm , corresponding velocities are $8 \mathrm{~cm} / \mathrm{s}$ and $6 \mathrm{~cm} / \mathrm{s}$ respectively. Its periodic time is

A particle starts oscillating simple harmonically from its equilibrium position with time period ' T '. What is the ratio of potential energy to kinetic energy of the particle at time $t=\frac{T}{12}$ ? $$\left(\sin \left(\frac{\pi}{6}\righ...

A simple pendulum of length ' $l$ ' has a brass bob attached at its lower end. It's period is ' T '. A steel bob of the same size, having density ' $x$ ' times that of brass, replaces the brass bob. Its length is then so changed that the pe...

The maximum velocity of a particle performing S.H.M. is '\(\mathrm{V}\)'. If the periodic time is made \(\left(\frac{1}{3}\right)^d\) and the amplitude is doubled, then the new maximum velocity of the particle will be

A rubber ball filled with water, having a small hole is used as the bob of a simple pendulum. The time period of such a pendulum

A particle is vibrating in S.H.M. with an amplitude of \(4 \mathrm{~cm}\). At what displacement from the equilibrium position is its energy half potential and half kinetic?

A spring has a certain mass suspended from it and its period for vertical oscillations is '\(T_1\)'. The spring is now cut in to two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is ...

Two S.H.Ms. are represented by equations \(\mathrm{y}_1=0.1 \sin \left(100 \pi \mathrm{t}+\frac{\pi}{3}\right)\) and \(\mathrm{y}_2=0.1 \cos (100 \pi \mathrm{t})\) The phase difference between the speeds of the two particles is

The bob of simple pendulum of length '\(L\)' is released from a position of small angular displacement \(\theta\). Its linear displacement at time '\(\mathrm{t}\)' is ( \(\mathrm{g}=\) acceleration due to gravity)

The displacement of a particle executing S.H.M. is \(x=\mathrm{a} \sin (\omega t-\phi)\). Velocity of the particle at time \(\mathrm{t}=\frac{\phi}{\omega}\) is \(\left(\cos 0^{\circ}=1\right)\)

A simple pendulum of length '\(l\)' and a bob of mass '\(\mathrm{m}\)' is executing S.H.M. of small amplitude '\(A\)'. The maximum tension in the string will be (\(\mathrm{g}=\) acceleration due to gravity)

A block of mass '\(M\)' rests on a piston executing S.H.M. of period one second. The amplitude of oscillations, so that the mass is separated from the piston, is (acceleration due to gravity, \(\mathrm{g}=10 \mathrm{~ms}^{-2}, \pi^2=10\) )

A light spring is suspended with mass \(m_1\) at its lower end and its upper end fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is \(T\) second. When a mass \(m_2\) is added t...

A uniform circular disc of mass \(12 \mathrm{~kg}\) is held by two identical springs. When the disc is slightly pressed down and released, it executes S.H.M. of period 2 second. The force constant of each spring is (nearly) (Take $$\pi^2=10...

A simple pendulum has a time period '\(T\)' in air. Its time period when it is completely immersed in a liquid of density one eighth the density of the material of bob is

A body of mass \(0.04 \mathrm{~kg}\) executes simple harmonic motion (SHM) about \(\mathrm{x}=0\) under the influence of force \(\mathrm{F}\) as shown in graph. The period of

A mass \(M\) is suspended from a light spring. An additional mass \(M_1\) added extends the spring further by a distance \(x\). Now, the combined mass will oscillate on the spring with period \(T=\)

Under the influence of force \(F_1\) the body oscillates with a period \(T_1\) and due to another force \(F_2\) body oscillates with period \(T_2\). If both forces acts simultaneously, then the resultant period is
(consider displacement is ...

Four massless springs whose force constants are \(2 \mathrm{~K}, 2 \mathrm{~K}, \mathrm{~K}\) and \(2 \mathrm{~K}\) respectively are attached to a mass \(\mathrm{M}\) kept on a frictionless plane as shown in figure, If mass \(M\) is displac...

A simple pendulum performs simple harmonic motion about \(\mathrm{x}=0\) with an amplitude '\(\mathrm{a}\)' and time period '\(T\)'. The speed of the pendulum at \(x=\frac{a}{2}\) is

A particle starts from mean position and performs S.H.M. with period 4 second. At what time its kinetic energy is \(50 \%\) of total energy?
\(\left(\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)\)

In a stationary lift, time period of a simple pendulum is '\(\mathrm{T}\)'. The lift starts accelerating downwards with acceleration \(\left(\frac{\mathrm{g}}{4}\right)\), then the time period of the pendulum will be

The time period of a simple pendulum inside a stationary lift is '\(T\)'. When the lift starts accelerating upwards with an acceleration \(\left(\frac{\mathrm{g}}{3}\right)\), the time period of the pendulum will be

For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at certain displacement '\(x\)' from the mean position. If '\(A\)' is the amplitude of S.H.M the value of '\(x\)' is

The upper end of the spring is fixed and a mass '\(m\)' is attached to its lower end. When mass is slightly pulled down and released, it oscillates with time period 3 second. If mass '\(\mathrm{m}\)' is increased by \(1 \mathrm{~kg}\), the ...

The amplitude of a particle executing S.H.M. is \(3 \mathrm{~cm}\). The displacement at which its kinetic energy will be \(25 \%\) more than the potential energy is

A simple harmonic progressive wave is represented by \(y=A \sin (100 \pi t+3 x)\). The distance between two points on the wave at a phase difference of \(\frac{\pi}{3}\) radian is

A body is executing a linear S.H.M. Its potential energies at the displacement '\(\mathrm{x}\)' and '\(\mathrm{y}\)' are '\(\mathrm{E}_1\)' and '\(E_2\)' respectively. Its potential energy at displacement \((\mathrm{x}+\mathrm{y})\) will be

A particle starts oscillating simple harmonically from its mean position with time period '\(T\)'. At time \(t=\frac{T}{12}\), the ratio of the potential energy to kinetic energy of the particle is $$\left(\sin 30^{\circ}=\cos 60^{\circ}=0....

In a medium, the phase difference between two particles separated by a distance '\(x\)' is \(\left(\frac{\pi}{5}\right)^{\text {c }}\). If the frequency of the oscillation of particles is \(25 \mathrm{~Hz}\) and the velocity of propagation ...

The time taken by a particle executing simple harmonic motion of period '\(\mathrm{T}\)', to move from the mean position to half the maximum displacement is

Two identical springs of constant '\(\mathrm{K}\)' are connected in series and parallel in shown in figure. A mass '\(\mathrm{M}\)' is suspended from them. The ratio of their frequencies is series to parallel combination will be

A body is executing S.H.M. under the action of force having maximum magntude \(50 \mathrm{~N}\). When its energy is half kinetic and half potential; the magnitude of the force acting on the particle is

A particle performing linear S.H.M. of amplitude \(0.1 \mathrm{~m}\) has displacement \(0.02 \mathrm{~m}\) and acceleration \(0.5 \mathrm{~m} / \mathrm{s}^2\). The maximum velocity of the particle in \(\mathrm{m} / \mathrm{s}\) is