Level 1

The magnitude of average acceleration in half time period from equilibrium position in a simple harmonic motion is,

The coefficient of friction between block of mass $m$ and $2\mathrm{m}$ is $\mu =2\tan \left(\theta \right)$. There is no friction between a block of mass $2\mathrm{m}$ and inclined plane. The maximum amplitude of two block system for which there is no relative motion between both the blocks-

The displacement of a particle is given by, $x={\cos }^2\omega t$. The motion is,

The time period of oscillation of a simple pendulum having length $L$ and mass of the bob $m$ is given as $T$. If the length of the pendulum is increased to $4L$ and the mass of the bob is increased to $2m$, then which one of the following is the new time period of oscillation?

In the case of a simple pendulum executing $\mathrm{SHM},$ at $t=0$, the bob is not at the mean position. The graph drawn between the tension $\left(T\right)$ in the string and time $\left(t\right)$ is

An object was found to make oscillations governed by the equation $y={\cos }^2\left(\omega t+\frac{\pi }{4}\right)-0.5$. The amplitude and angular frequency of these oscillations, respectively, are

A body of mass $8 \mathrm{kg}$ moving with a velocity of $2 {\mathrm{ms}}^{-1}$ comes to the rest, after compressing a spring placed on a frictionless table. If the spring constant is $5000 {\mathrm{Nm}}^{-1}$ then compression produced in the spring shall be

Two masses are connected by a spring as shown in the figure. One of the masses was given velocity $v=2k$ as shown in figure where $k$ is the spring constant. Then maximum extension in the spring will be