$Y = A \sin \left(\omega t +\phi_{0}\right)$ is the time-displacement equation of a SHM. At $t=0$ the displacement of the particle is $Y =\frac{ A }{2}$ and it is moving along negative $x$ -direction. Then the initial phase angle $\phi_{0}$ will be ...... .
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A particle is doing simple harmonic motion of amplitude $0.06 \mathrm{~m}$ and time period $3.14 \mathrm{~s}$. The maximum velocity of the particle is. . . . .. . $\mathrm{cm} / \mathrm{s}$.
A particle of mass $4 \,kg$ moves simple harmonically such that its $P E(U)$ varies with position $x$, as shown. The period of oscillations is ............
A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is $\frac{2}{{\sqrt 5 }}$. After how many collisions the amplitude of vibration will become less than $60°$
A clock which keeps correct time at ${20^o}C$, is subjected to ${40^o}C$. If coefficient of linear expansion of the pendulum is $12 \times {10^{ - 6}}/^\circ C$. How much will it gain or loose in time
A particle is performing simple harmonic motion along $x$ -axis with amplitude $4\, cm$ and time period $1.2\, sec$. The minimum time taken by the particle to move from $x = 2\, cm$ to $x =+ 4 \,cm$ and back again is given by .... $s$
The instantaneous displacement of a simple pendulum oscillator is given by $x = A\,\cos \,\left( {\omega t + \frac{\pi }{4}} \right)$ . Its speed will be maximum at time
In damped oscillations, damping force is directly proportional to speed of oscillator. If amplitude becomes half of its maximum value in $1 \,s$, then after $2 \,s$ amplitude will be $\left(A_0-\right.$ initial amplitude)