Embibe Experts Solutions for Chapter: Simple Harmonic Motion, Exercise 7: Exercise (Previous Year Questions)

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

Out of the following functions representing the motion of a particle, which one represents S.H.M.?

(1) $y=\sin \omega t-\cos \omega t$
(2) $y={\sin }^3\omega t$
(3) $y=5\cos \left(\frac{3\pi }{4}-3\omega t\right)$
(4) $y=1+\omega t+{\omega }^2{t}^2$

A particle is executing SHM along a straight line. Its velocities at distances $x_1$ and $x_2$ from the mean position are $v_1$ and $v_2$, respectively. Its time period is

A body of mass $m$ is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass $m$ is slightly pulled down and released, it oscillates with a time period of $3 \mathrm{s}$. When the mass $m$ is increased by $1 \mathrm{kg}\text{,}$ the time period of oscillations becomes $5 \mathrm{s}$. The value of $m \mathrm{in} \mathrm{kg}$ is

In an angular S.H.M. angular amplitude of oscillation is $\pi$ $\mathrm{rad}$ and the time period is$0.4$ $\mathrm{s}$ then calculate its angular velocity at angular displacement $\frac{\pi }{2}$ $\mathrm{rad}$.

A spring of force constant $k$ is cut into lengths of ratio $1:2:3$. They are connected in series and the new force constant is $k^{\text{'}}$. Then, they are connected in parallel and force constant is $k^{\text{'}\text{'}}$. Then, $k^{\text{'}}:k^{\text{'}\text{'}}$ is,

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

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 $20 \mathrm{m} {\mathrm{s}}^{-2}$ at a distance of $5 \mathrm{m}$ from the mean position. The time period of oscillation is