A particle's velocity is given by $v = 4 - 2t$, where $t$ is in seconds and $v$ is in m/s. If the particle starts at $x = 2$ m at $t = 0$, at what time does the particle instantaneously change its direction of motion?

A particle executes SHM in a line 4 cm long. Its velocity when passing through the centre of line is $12cm/s$ . The period will be

A particle executes S.H.M. with a period of 6 second and amplitude of 3 $cm$ . Its maximum speed in $cm$/$s$ is

If the differential equation given by $\frac{{{d^2}y}}{{d{t^2}}} + 2k\frac{{dy}}{{dt}} + {\omega ^2}y = {F_0}\sin pt$ Describes the oscillatory motion of body in a dissipative medium under the influence of a periodic force, then the state of maximum amplitude of the oscillation is a measure of

The velocities of a body executing $SHM$ are $3\,cm/s$ and $4\,cm/s$. When the displacements are $4\,cm$ and $3\,cm$ respectively then period is

The amplitude of vibration of a particle is given by ${a_m} = ({a_0})/(a{\omega ^2} - b\omega + c);$ where ${a_0},a,b$ and c are positive. The condition for a single resonant frequency is

A particle's position is given by $\vec r = A\cos \left( {\omega t + \phi } \right)\hat x + A\sin \left( {\omega t + \phi } \right)\hat y$, where $A$, $\omega$, and $\phi$ are constants. What type of motion does the particle exhibit?

Displacement-time equation of a particle executing SHM is, $x = 4\sin \omega t + 3\sin \,\,(\omega t + \pi /3)$ Here $x$ is in centimeter and t in second. The amplitude of oscillation of the particle is approximately

The height of a swing changes during its motion from 0.1 $m$ to 2.5 $m$. The minimum velocity of a boy who swings in this swing is

The amplitude of SHM $\;y = 2\left( {\sin 5\,\,{\rm{\pi }}t + \sqrt 2 {\rm{cos}}\,\,{\rm{\pi }}t} \right)$ is

The speed of the particle on a reference circle of radius $R$ is $V$ . The time period of oscillations of the projection on a diameter of the circle is