Velocity & Acceleration in SHM

A simple pendulum performs simple harmonic motion about $x = 0$ with an amplitude 'A' and angular frequency $\omega$. The speed of pendulum at $x = \frac{A}{8}$ will be.

A particle is performing S.H.M. about $x = 0$, with an amplitude $a$ and time period $T$. The speed of the particle at $x = \frac{a}{3}$ will be

A particle is performing simple harmonic motion about $x = 0$ with an amplitude '$a$' and periodic time T. The speed of the particle at $x = \frac{a}{3}$ will be

A particle executing simple harmonic motion starts from mean position with amplitude '$A$' and periodic time '$T$'. At what displacement is its speed one-fourth of the maximum speed?

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 $\frac{x}{7}\text{ s}$, the value of $x$ is ______.

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

Two particles performing simple harmonic motions of maximum accelerations, $1$ m/s$2$ and $100$ m/s$2$, have the same amplitudes. The ratio of their angular frequencies is

A body of mass $0.4$ kg performs simple harmonic motion. It experiences a restoring force of $0.4$ N when its displacement from the mean position is 4 cm. The force constant and magnitude of acceleration respectively are

A particle executes S.H.M. with time period $16$ s. At time $t = 2$ s, the particle crosses the mean position while at $t = 4$ s, velocity is $4$ m/s. The amplitude of motion (in m) is $\left(\sin 45^\circ = \frac{1}{\sqrt{2}}\right)$

A particle executes linear S.H.M. with amplitude $4$ cm. The magnitude of velocity and acceleration is equal when it is at $3$ cm from mean position. Time period is

The velocity of a particle executing SHM varies with displacement ($x$) as $4v^2 = 50 - x^2$. The time period of oscillations is $x/7$ s.

The value of $x$ is (Take $\pi = 22/7$)

A particle executing linear S.H.M. has velocities $V_1$ and $V_2$ at distance $x_1$ and $x_2$ respectively, from the mean position, its angular velocity is

Consider a spring-mass simple harmonic oscillator in one dimension. The mass of the particle is $m\text{ kg}$ and the spring constant is $k\text{ N m}^{-1}$. At a given instant, the extension of the spring is $x$-meter and the speed of the particle is $v\text{ m s}^{-1}$. On the $x - v$ plane, if the graph of $v$ as a function of $x$ is a circle, then the correct option is:

A simple pendulum starts oscillating simple harmonically from its mean position ( $x = 0$) with amplitude ' $a$ ' and periodic time ' $T$ '. The magnitude of velocity of pendulum at $x = \frac{a}{2}$ is

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 $V$max. The displacement of the particle at that instant is

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

A particle is performing S.H.M. starting from extreme position. Graphical representation shows that between displacement and acceleration, there is a phase difference of

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

A particle executes a linear S.H.M. In two of its positions the velocities are $V_1, V_2$ and accelerations are $a_1$ and $a_2$ respectively $(0 < a_1 < a_2)$. The distance between the positions is

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

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

The maximum velocity of a particle, executing S.H.M. with an amplitude 7 mm is $4.4\text{ m s}^{-1}$ The period of oscillation is $\left[\pi = \frac{22}{7}\right]$

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

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 particle is doing simple harmonic motion of amplitude $0.06\text{ m}$ and time period $3.14\text{ s}$. The maximum velocity of the particle is _________ $\text{cm/s}$.

A particle performing S.H.M. starts from equilibrium position and its time period is 12 second. After 2 seconds its velocity is $\pi\text{ m/s}$. Amplitude of the oscillation is

$\left[\sin 30^\circ = \cos 60^\circ = 0.5,\ \sin 60^\circ = \cos 30^\circ = \sqrt{3}/2\right]$

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

The displacement of a particle executing SHM is given by $x = 10\sin\left(\omega t + \frac{\pi}{3}\right)\text{ m}$. The time period of motion is $3.14\text{ s}$. The velocity of the particle at $t = 0$ is _______ $\text{m/s}$.

A particle performs simple harmonic motion with amplitude $A$. Its speed is increased to three times at an instant when its displacement is $\frac{2A}{3}$. The new amplitude of motion is $\frac{nA}{3}$. The value of $n$ is ___________.

A particle executes simple harmonic motion with an amplitude of $4\text{ cm}$. At the mean position, velocity of the particle is $10\text{ cm/s}$. The distance of the particle from the mean position when its speed becomes $5\text{ cm/s}$ is $\sqrt{\alpha}\text{ cm}$, where $\alpha =$ ________.

A particle executing S.H.M. has velocities ' $V_1$ ' and ' $V_2$ ' at distances ' $x_1$ ' and ' $x_2$ ' respectively, from the mean position. Its frequency is

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 $8\text{ cm/s}$ and $6\text{ cm/s}$ respectively. Its periodic time is

A particle is executing a linear simple harmonic motion. Let ' $V_1$ ' and ' $V_2$ ' are its speed at distance ' $x_1$ ' and ' $x_2$ ' from the equilibrium position. The amplitude of oscillation is

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4\text{ m}, 2\text{ m s}^{-1}$ and $16\text{ m s}^{-2}$ at a certain instant. The amplitude of the motion is $\sqrt{x}\text{ m}$ where $x$ 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 from the platform? [Take $g = 10\text{ m/s}^2$]

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 between the two positions is

A particle performs linear S.H.M. At a particular instant, velocity of the particle is ' $u$ ' and acceleration is ' $a_1$ ' while at another instant velocity is ' $v$ ' and acceleration is ' $a_2$ ' $(0 < a_1 < a_2)$. The distance between the two positions is

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

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

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

The velocity of a particle executing SHM varies with displacement $(x)$ as $4v^2 = 50 - x^2$. The time period of oscillations is $\frac{x}{7}\text{ s}$. The value of $x$ is ___________. $($ Take $\pi = \frac{22}{7})$

A rectangular block of mass $5\text{ kg}$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $1\text{ m}$ and time period $3.14\text{ s}$. The maximum force exerted by spring on block is _________ N

A particle of mass 250 g executes a simple harmonic motion under a periodic force $F = (-25x)\text{ N}$. The particle attains a maximum speed of 4 m/s during its oscillation. The amplitude of the motion is ___________ cm.

The $x\text{-}t$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t = 2\text{ s}$ is:

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, $g = 10\text{ m s}^{-2},\ \pi^2 = 10$)

The equation of a particle executing simple harmonic motion is given by $x = \sin\pi\left(t + \frac{1}{3}\right)\text{ m}$. At t = 1s, the speed of particle will be

(Given: $\pi$ = 3.14)

A particle executing SHM has its velocity $20\text{ cm s}^{-1}$ at mean position and acceleration of $25\text{ cm s}^{-2}$ at one of its extreme position. The amplitude of the particle will be ____ cm.

When a particle executes Simple Harmonic Motion, the nature of graph of velocity as a function of displacement will be:

A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air jet when it is at 5 cm from its mean position. The new amplitude of vibration is $\sqrt{x}$ cm. The value of x is _____________.

A particle executing S.H.M starts from the mean position. Its amplitude is 'A' and time period '$T$'. At what displacement its speed is one-fourth of the maximum speed?

A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of the particle when its speed is half of maximum speed is $\frac{\sqrt{x}a}{2}$. The value of x is __________.

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

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 particle of mass 5 g 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

A particle executes S.H.M., the graph of velocity as a function of displacement is:

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:

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

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

A particle is making simple harmonic motion along the X-axis. If at a distances x1 and x2 from the mean position the velocities of the particle are v1 and v2 respectively. The time period of its oscillation is given as:

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

The displacement time graph of a particle executing S.H.M is given in figure:

(sketch is schematic and not to scale)

Which of the following statements is/are true for this motion?

(A) The force is zero at t = $\frac{3T}{4}$

(B) The acceleration is maximum at t = T

(C) The speed is maximum at t = $\frac{T}{4}$

(D) The P.E. is equal to K.E. of the oscillation at t = $\frac{T}{2}$

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?

A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is -

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

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m s–2 at a distance of 5 m from the mean position. The time period of oscillation is

A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in second is

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s−1. At, t = 0 the displacement is 5 m. What is the maximum acceleration? The initial phase is $\frac{\pi}{4}$.

A particle performs simple harmonic motion with amplitude $A.$ Its speed is trebled at the instant that it is at a distance $\frac{2A}{3}$ from equilibrium position. The new amplitude of the motion is:

In an engine the piston undergoes vertical simple harmonic motion with amplitude 7 cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to:

A particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$. Then, its time period of vibration will be

A particle is executing SHM along a straight line. Its velocities at distances x1 and x2 from the mean position are V1 and V2 respectively. Its time period is

The oscillation of a body on a smooth horizontal surface is represented by the equation, X = A cos$(\omega t)$

where X = displacement at time t

$\omega$ = frequency of oscillation

Which one of the following graphs shows correctly the variation of a with t?

Here a = acceleration at time t

T = time period

A particle of mass m oscillates along x-axis according to equation x = asin$\omega$t. The nature of the graph between momentum and displacement of the particle is

A mass $m = 1.0$ kg is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is 500 N/m. What is the amplitude A of the motion, so that the mass m tends to get detached from the pan? (Take $g = 10$ m/s$2$ ). The spring is stiff enough so that it does not get distorted during the motion.

A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T. The speed of the pendulum at x = a/2 will be

If $x, v$ and $a$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $T,$ then, which of the following does not change with time?

$-$1

Two simple harmonic motions of angular frequency 100 and 1000 rad s have the same displacement amplitude. The ratio of their maximum acceleration is

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is

A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible.

When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take g = 10 m/s2).

The maximum velocity of a particle, executing simple harmonic motion with an amplitude $7\text{ mm},$ is $4.4\text{ m/s}.$ The period of oscillation is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency $\omega.$ The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

A particle executing simple harmonic motion of amplitude $5\text{ cm}$ has maximum speed of $31.4\text{ cm/s}$. The frequency of its oscillation is

Which one of the following statements is true for the speed v and the acceleration a of a particle executing simple harmonic motion?

A particle starts with S.H.M. from the mean position as shown in the figure. Its amplitude is $A$ and its time period is $T$. At one time, its speed is half that of the maximum speed. What is this displacement?

If a simple harmonic oscillator has got a displacement of $0.02\text{ m}$ and acceleration equal to $2.0\text{ m/s}^2$ at any time, the angular frequency of the oscillator is equal to

A body is executing simple harmonic motion. When the displacements from the mean position is $4\text{ cm}$ and $5\text{ cm}$, the corresponding velocities of the body is $10\text{ cm/sec}$ and $8\text{ cm/sec}$. Then the time period of the body is