A body moves in a plane such that its displacement vector is given by $\vec{r} = (3t^2 - 2)\hat{i} + (2t^3 + 1)\hat{j}$. At what time is the velocity vector perpendicular to the acceleration vector?

The total energy of a particle, executing simple harmonic motion is Where x is the displacement from the mean position.

The displacement of a particle executing simple harmonic motion is given by $y\, = \,{A_0}\, + \,A\sin \omega t\, + \,B\cos \,\omega t\,$. Then the amplitude of its oscillation is given by:

The equation of motion for a particle in SHM is $x = 4 \sin(\frac{\pi}{2} t + \pi)$. Find the maximum displacement and the time taken for one complete oscillation.

The particle executes $SHM$ with an amplitude of $0.2\,m$. Its displacement when its phase is ${90^0}$ is

A simple pendulum oscillates with a displacement given by $x = 0.1 \sin(4\pi t)$. What are the amplitude and frequency of the pendulum's motion?

The displacement of a partied performing in SHM is $x = 3\sin (20\pi t) + 4\cos (20\pi t){\rm{ cm}}{\rm{.}}$ Its amplitude of oscillation is

The particle executes $SHM$ with an amplitude of $0.2\,m$. Its displacement when its phase is ${90^0}$ is

Displacement between maximum potential energy position and maximum kinetic energy position for a particle executing S.H.M. is

In case of a forced vibration, the resonance wave becomes very sharp when the

A particle moves according to the law,$x = rcos\frac{{\pi t}}{{2.}}$ The distance covered by it the time interval between t= 0 to t=3s is