Level 2

The weight suspended from a spring oscillates up and down. The acceleration of weight will be zero at

When a body is in $SHM$, then match the following.

One end of a spring of force constant $k$ is fixed to a vertical wall and the other to a block of mass $m$ resting on a smooth horizontal surface. There is another wall at a distance $x_0$, from the block. The spring is then compressed by $2x_0$ and released. The time taken by the block to strike the other wall is

A simple harmonic oscillator of frequency $1 \mathrm{Hz}$ has a phase of $1$ radian. By how much should the origin be shifted in time so as to make the phase of the oscillator vanish. (time in seconds).

Two clocks $A$ and $B$ are synchronized to show the same time on earth. Clock $A$ is based on oscillations of spring and clock $B$ is based on a pendulum motion. If these two clocks are taken to the surface of the moon, then

The amplitude of a damped oscillator decreases to$0.9$ times its original magnitude in $5 \mathrm{s}$. In another $10 \mathrm{s}$ it will decrease to $\alpha$ times its original magnitude, then $\alpha$ is equal to
 

The decrease in amplitude with time of an under damped oscillator is

A particle of mass $0.1 \mathrm{kg}$ is executing simple harmonic motion of amplitude $0.1 \mathrm{m}$. When the particle passes through the mean position, its kinetic energy is $8\times {10}^{-3} \mathrm{J}$. If the initial phase is $45°,$ the equation of its motion is (Assume, $x \left(t\right)$ as the position of the particle at time $t$)