SHM Questions

A particle of mass $m$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time?

Out of the following functions representing motion of a particle, which represents SHM?(A) $y=\sin \omega t-\cos \omega t$ (B) $y={\sin }^3\omega t$ (C) $y=5\cos \left(\frac{3\pi }{4}-3\omega t\right)$ (D) $y=1+\omega t+{\omega }^2{t}^2$

Which of the following functions represents a simple harmonic oscillation?

A particle executes simple harmonic oscillation with an amplitude $a$. The period of oscillation is $T$. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is:

The particle executing simple harmonic motion has a kinetic energy $K_0{\cos }^2\omega t$. The maximum values of the potential energy and the total energy are respectively:

A mass of $2.0\text{kg}$ is put on a flat pan attached to a vertical spring. The spring constant is $200\text{N/m}$. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan? ($g=10{\text{m/s}}^2$)

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

Two Simple Harmonic Motions of angular frequency $100{\text{rad s}}^{-1}$ and $1000{\text{rad s}}^{-1}$ have the same displacement amplitude. The ratio of their maximum accelerations is:

A point performs simple harmonic oscillation of period $T$ and the equation of motion is given by $x=a\sin (\omega t+\pi /6)$. After the elapse of what fraction of the time period will the velocity of the point be equal to half of its maximum velocity?

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:

Which one of the following equations of motion represents simple harmonic motion?

The displacement of a particle along the x-axis is given by $x=a{\sin }^2\omega t$. The motion of the particle corresponds 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: