Oscillations practice · Medium

A particle moves so that its acceleration a is given by $a = - bx$ where $x$ is displacement from equilibrium position and b is a non-negative real constant. The time period of oscillation of the particle is

When an oscillator completes 50 oscillations, its amplitude reduces to $\frac{1}{3}$ times of the initial value. The amplitude, when it completes 100 oscillations will be

A solid sphere of radius $R$ and density $\rho$ is attached to one end of a massless spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3 \rho$. The complete arrangement is placed in a liquid of density $2 \rho$ and is allowed to reach equilibrium. The correct statement is

Two particles are executing S.H.M. The equations of their motion are $y_1=10 \sin \left(\omega t+\frac{\pi T}{4}\right), y_2=25 \sin \left(\omega t+\frac{\sqrt{3} \pi T}{4}\right)$.
What is the ratio of their amplitude?

When the displacement is half the amplitude, the ratio of potential energy to the total energy is

The displacement y of a particle executing periodic motion is given by $y = 4{\cos ^2}\left( {t/2} \right)\sin \left( {1000t} \right)$ . This expression may be considered to be a result of the superposition of…….. independent harmonic motions

A particle is executing simple harmonic motion with an amplitude A and time period T. The displacement of the particle after 2T period from its initial position is

The kinetic energy of a particle executing S.H.M. is 16 J when it is at its mean position. If the mass of the particle is 0.32 kg, then what is the maximum velocity of the particle

The potential energy of a particle in SHM is:

${T_0}$ is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to $\frac{1}{{16}}$ times of its initial value, then the modified time period is

A simple pendulum consists of a mass attached to a light string $l.$ if the system is oscillating through small angles which of the following is true?

The relation between acceleration and displacement of four particles are given below. Which one of the particles is executing simple harmonic motion?

Force acting on a body moving along $x$-axis is given as $F=-k x^3$, where $x$ is the displacement of the body from its mean position. The motion of body is:

Statement-1: Time period of spring pendulum is the same whether in an accelerated or in an inertial frame of reference.
Statement-2: Mass of the bob of spring pendulum and spring constant of the spring are independent of the acceleration of the frame of reference.

The motion of a simple pendulum executing S.H.M. is represented by the following equation.
$y = A\sin \left( {\pi t + \phi } \right)$, where time is measured in second. The length of pendulum is

In the differential equation of linear simple harmonic motion, $\frac{d^2 x}{d t^2}+\omega^2 x=0$, the term $\omega^2$ represents

The velocity vector $v$ and displacement vector $x$ of a particle executing SHM are related as $\frac{v d v}{d x}=-\omega^2 x$ with the initial condition $v=v_0$ at $x=0$. The velocity $v$ when displacement is $x$, is

A simple wave motion is represented by $y=5(\sin \,4 \,\pi\, t+\sqrt{3} \cos \,4 \,\pi \,t)$. Its amplitude is

What is the effect on the time period of a simple pendulum if the mass of the bob is doubled

Starting from $y = A$ $\sin \,\,\omega t\mathrm{ }or\mathrm{ }y = A\,\,\cos \,\,\omega t$

The physical quantity conserved in simple
harmonic motion is

A mass $m$ attached to a spring of spring constant $k$ is stretched a distance $x_0$ from its equilibrium position and released with no initial velocity. The maximum speed attained by the mass in its subsequent motion and the time at which this speed would be attained are respectively,

Assertion: Amplitude of a forced vibration can never reach infinity.
Reason: The driving frequency cannot be increased beyond a certain limit.

Consider the following statements : The total energy of a particle executing simple harmonic motion depends on its I. Amplitude II. Period III. Displacement Of these statements

For Simple Harmonic Oscillator, the potential energy is equal to kinetic energy

A particle executing SHM while moving from one extremity is found at distances $x_1, x_2$ and $x_3$ from the centre at the end of three successive seconds. The time period of oscillation is

A particle moves in x-y plane according to rule x=a sin⁡ωt and y=a cos⁡ωt. The particle follows

A particle executes $SHM$ with an amplitude of $5\,cm$. The percentage of its energy which is potential energy at a displacement of $1\,cm$ from the mean position is

The amplitude of oscillations of a simple harmonic oscillator of mass 100 gram having an angular frequency of $10\,\,rad\,{s^{ - 1}}$ with a total mechanical energy of is

Two pendulums of length 1 m and 16 m start vibrating one behind the other from the same stand. At some instant, the two are in the mean position in the same phase. The time period of shorter pendulum is T. the minimum time after which the two threads of the pendulum will be one behind the other is?