Simple Harmonic Motion

Two particles ' $A$ ' and ' $B$ ' execute SHMs of periods ' $T$ ' and $\frac{3 T}{2}$. If they start from the mean position then the phase difference between them, when the particle ' $A$ ' completes two oscillations will be

The displacement of particle in S.H.M. is $\mathrm{x}=\mathrm{A} \cos (\omega \mathrm{t}+\pi / 6)$. Its speed will be maximum at time $\left(\sin 90^{\circ}=1\right)$

As shown in the figure, $S_1$ and $S_2$ are identical springs with spring constant K each. The oscillation frequency of the mass ' $m$ ' is ' $f$ '. If the spring $\mathrm{S}_2$ is removed, the oscillation frequency will become

Two simple pendulums have first (A) bob of mass ' $M_1$ ' and length ' $L_1$ ', second (B) of mass ' $\mathrm{M}_2$ ' and length ' $\mathrm{L}_2$ '. $\mathrm{M}_1=\mathrm{M}_2$ and $\mathrm{L}_1=2 \mathrm{~L}_2$. If their total energies are...

A particle starts oscillating simple harmonically from its mean position with time period ' $T$ '. At time $\mathrm{t}=\frac{\mathrm{T}}{6}$, the ratio of the potential energy to kinetic energy of the particle is
$$ \left[\sin 30^{\circ}=\c...

The amplitude of a damped oscillator becomes $\left(\frac{1}{3}\right)^{\mathrm{rd}}$ of original amplitude in 2 seconds. If its amplitude after 6 second become $\left(\frac{1}{n}\right)$ times the original amplitude, the value of $n$ is ( ...

A particle is executing linear S.H.M. starting from mean position. The ratio of the kinetic energy to the potential energy of the particle at a point of half the amplitude is

A particle is executing S.H.M. of amplitude ' $A$ '. When the potential energy of the particle is half of its maximum value during the oscillation, its displacement from the equilibrium position is

An object of mass 0.2 kg executes simple harmonic oscillations along the x -axis with frequency of $\left(\frac{25}{\pi}\right) \mathrm{Hz}$. At the position $x=0.04 \mathrm{~m}$, the object has kinetic energy 1 J and potential energy 0.6 J...

The motion of the particle is given by the equation $\mathrm{x}=\mathrm{A} \sin \omega \mathrm{t}+\mathrm{B} \cos \omega \mathrm{t}$.
The motion of the particle is

For a particle performing S.H.M.; the total energy is ' $n$ ' times the kinetic energy, when the displacement of a particle from mean position is $\frac{\sqrt{3}}{2} \mathrm{~A}$, where A is the amplitude of S.H.M. The value of ' $n$ ' is

A particle performing linear S.H.M. has period 8 seconds. At time $\mathrm{t}=0$, it is in the mean position. The ratio of the distances travelled by the particle in the $1^{\text {st }}$ and $2^{\text {nd }}$ second is $\left(\cos 45^{\cir...

A small spherical ball of radius ' $r$ ' is rolling on a curved surface which is frictionless and has a radius of curvature ' R '. Its motion is simple harmonic. Then its tine period of oscillation is proportional to ( $\mathrm{g}=$ acceler...

A particle executes S.H.M. starting from the mean position. Its amplitude is ' a ' and its periodic time is ' $T$ '. At a certain instant, its speed ' $u$ ' is half that of maximum speed $\mathrm{V}_{\text {max }}$. The displacement of the ...

A simple pendulum has time period ' $\mathrm{T}_1$ '. The point of suspension is now moved upward according to equation $\mathrm{y}=\mathrm{kt}^2$ where $\mathrm{k}=1 \mathrm{~m} / \mathrm{s}^2$. If new time period is ' $\mathrm{T}_2$ ' the...

Two simple harmonic motions of angular frequency $300 \mathrm{rad} / \mathrm{s}$ and $3000 \mathrm{rad} / \mathrm{s}$ have same amplitude. The ratio of their maximum accelerations is

A mass $m$ is suspended from a spring of negligible mass. The spring is pulled a little and then released, so that mass executes S.H.M. of time period $T$. If the mass is increased by $m_0$, the periodic time becomes $\frac{5 \mathrm{~T}}{4...

The length of the simple pendulum is made 3 times the original length. If ' T ' is its original time period, then the new time period will be

The period of S. H.M. of a particle is 16 second. The phase difference between the positions at $\mathrm{t}=2 \mathrm{~s}$ and $\mathrm{t}=4 \mathrm{~s}$ will be

A particle oscillates in straight line simple harmonically with period 8 second and amplitude $4 \sqrt{2} \mathrm{~m}$. Particle starts from mean position. The ratio of the distance travelled by it in $1^{\text {st }}$ second of its motion ...

If the period of a oscillation of mass ' m ' suspended from a spring is 2 s , then the period of suspended mass ' 4 m ' with the same spring will be

A mass $x$ gram is suspended from a light spring. It is pulled in downward direction and released so that mass performs S.H.M. of period T. If mass is increased by Y gram, the period becomes $\frac{4 \mathrm{~T}}{3}$. The ratio of $\mathrm{...

A particle executes a linear S.H.M. In two of its positions the velocities are $\mathrm{V}_1, \mathrm{~V}_2$ and accelerations are $\mathrm{a}_1$ and $\mathrm{a}_2$ respectively $\left(0

A mass attached to a spring performs S.H.M. whose displacement is $\mathrm{x}=3 \times 10^{-3} \cos 2 \pi \mathrm{t}$ metre. The time taken to obtain maximum speed for the first time is

The time period of a simple pendulum inside a stationary lift is $\sqrt{3}$ second. When the lift moves upwards with an acceleration $g / 3$, the time period will be ( $\mathrm{g}=$ acceleration due to gravity)

' $P$ ' and ' $Q$ ' are fixed points in same plane and mass ' $m$ ' is tied by string as shown in figure. If the mass is displaced slightly out of this plane and released, it will oscillate with time period $(\mathrm{PQ}=2 \mathrm{~d}, \mat...

A mass suspended from a vertical spring performs S.H.M. of period 0.1 second. The spring is unstretched at the highest point of suspension. Maximum speed of the mass is (Gravitational acceleration $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ...

For a particle performing; S.H.M. the displacement - time graph is shown.

For that particle the force - time graph is correctly shown in graph

If the length of the oscillating simple pendulum is made $\frac{1}{3}$ times the original keeping amplitude same then increase in its total energy at a place will be

A vertical spring oscillates with period 6 second with mass $m$ is suspended from it. When the mass is at rest, the spring is stretched through a distance of (Take, acceleration due to gravity, $\mathrm{g}=\pi^2=10 \mathrm{~m} / \mathrm{s}^...

A particle is performing S.H.M. with an amplitude 4 cm . At the mean position the velocity of the particle is $12 \mathrm{~cm} / \mathrm{s}$. When the speed of the particle becomes $6 \mathrm{~cm} / \mathrm{s}$, the distance of the particle...

In S.H.M. the displacement of a particle at an instant is $Y=A \cos 30^{\circ}$, where $A=40 \mathrm{~cm}$ and kinetic energy is 200 J . If force constant is $1 \times 10^{\times} \mathrm{N} / \mathrm{m}$, then x will be $\left(\cos 30^{\ci...

A particle is executing a linear simple harmonic motion. Let ' $\mathrm{V}_1$ ' and ' $\mathrm{V}_2$ ' are its speed at distance ' $x_1$ ' and ' $x_2$ ' from the equilibrium position. The amplitude of oscillation is

Two bodies A and B of equal mass are suspended from two separate massless springs of spring constants $\mathrm{K}_1$ and $\mathrm{K}_2$ respectively. The two bodies oscillate vertically such that their maximum velocities are equal. The rati...

The velocity of particle executing S.H.M. varies with displacement $(\mathrm{x})$ as $4 \mathrm{~V}^2=50-\mathrm{x}^2$. The time period of oscillation is $\frac{x}{7}$ second. The value of ' $x$ ' is (Take $\pi=\frac{22}{7}$)

A simple pendulum of length $l_1$ has time period $\mathrm{T}_1$. Another simple pendulum of length $l_2\left(l_1>l_2\right)$ has time period $T_2$. Then the time period of the pendulum of length $\left(l_1-l_2\right)$ will be

The maximum velocity and maximum acceleration of a particle performing a linear S.H.M. is ' $\alpha$ ' and ' $\beta$ ' respectively. Then the path length of the particle is

A mass ' $m$ ' attached to a spring oscillates with a period of 3 second. If the mass is increased by 0.6 kg , the period increases by 3 second. The initial mass ' $m$ ' is equal to

A tube of uniform bore of cross-sectional area ' $A$ ' has been set up vertically with open end facing up. Now ' $M$ ' gram of a liquid of density ' $d$ ' is poured into it. The column of liquid in this tube will oscillate with a period ' T...

A small sphere oscillates simple harmonically in a watch glass whose radius of curvature is 1.6 m . The period of oscillation of the sphere in second is (acceleration due to gravity, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

When a particle in linear S.H.M. completes two oscillations, its phase increases by

Frequency of a particle performing S.H.M. is 10 Hz . The particle is suspended from a vertical spring. At the highest point of its oscillation the spring is unstretched. Maximum speed of the particle is $\left(\mathrm{g}=10 \mathrm{~m} / \m...

The period of a simple pendulum gets doubled when

Three masses $500 \mathrm{~g}, 300 \mathrm{~g}$ and 100 g are suspended at the end of spring as shown in figure and are in equilibrium. When the 500 g mass is removed, the system oscillates with a period of 3 second. When the 300 g mass is ...

A particle is performing simple harmonic motion and if the oscillations are Camped oscillations then the angular frequency is given by

Choose the correct answer.
When a point of suspension of pendulum is moved vertically upward with acceleration ' $a$ ', its period of oscillation

For a body performing simple harmonic motion, its potential energy is $\mathrm{E}_{\mathrm{x}}$ at displacement x and $\mathrm{E}_{\mathrm{y}}$ at displacement y from mean position. The potential energy $E_0$ at displacement $(x+y)$ is

A spring has a certain mass suspended from it and its period of vertical oscillations is $T_1$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now $\...

The displacement of a particle performing S.H.M. is given by $Y=A \cos [\pi(t+\phi)]$. If at $\mathrm{t}=0$, the displacement is $\mathrm{y}=2 \mathrm{~cm}$ and velocity is $2 \pi \mathrm{~cm} / \mathrm{s}$, the value of amplitude $A$ in cm...

A particle executing S.H.M. has velocities ' $\mathrm{V}_1$ ' and ' $\mathrm{V}_2$ ' at distances ' $x_1$ ' and ' $x_2$ ' respectively, from the mean position. Its frequency is