Oscillations

For a particle in SHM, the displacement $x$ of the particle as a function of time $t$ is given as $x=A \sin (2 \pi t)$. Here $x$ is in cm and $t$ is in seconds. Let the time taken by the particle to travel from $x=0$ to…

A particle executes simple harmonic motion with a period of $8 \mathrm{~s}$ and amplitude $4 \mathrm{~cm}$. Its maximum speed in $\mathrm{cm} / \mathrm{s}$, is

In damped oscillation, graph between velocity and position will be

Assertion : If a pendulum is suspended in a lift and lift is falling freely, then its time period becomes infinite. Reason : Free falling body has acceleration equal to acceleration due to gravity.

Assertion : In simple harmonic motion, kinetic energy and potential energy become equal when the displacement is $(1 / \sqrt{2})$ times the amplitude. Reason : In simple harmonic motion, kinetic energy is zero when…

Assertion : When a pendulum is made to oscillate on the surface of the Moon, its time period increases. Reason : Moon is much smaller as compared to Earth.

A particle is performing simple harmonic motion with angular frequency 5000 radian/second and amplitude $2 \mathrm{~cm}$ and mass of $1 \mathrm{~kg}$. Find the total energy of oscillation?

Assertion : A particle in $x-y$ plane is related by $x=a \sin \omega t$ and $y=a(1-\cos \omega t)$, where $a$ and $\omega$ are constants, then the particle will have parabolic motion. Reason : A particle under the…

Four massless springs whose force constants are $2 k, 2 k, k$ and $2 k$ respectively are attached to a mass $M$ kept on a frictionless plane as shown in the figure. If the mass $M$ is displaced in the horizontal…

Assertion : The graph of potential energy and kinetic energy of a particle in SHM with respect to position is a parabola. Reason : Potential energy and kinetic energy do not vary linearly with position.

A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period $T$. If the mass is increased by $m$,…

The displacement of a particle executing SHM is given by $y=0.25 \sin 200 t \mathrm{~cm}$. The maximum speed of the particle is