The piston in the cylinder head of locomotive has a stroke of $6\,m$ (which is twice the amplitude). If the piston executing simple harmonic motion with an angular frequency of $200\, rad\, min^{-1}$, its maximum speed is .... $ms^{-1}$
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A simple pendulum of mass $m$ executes $S.H.M.$ with total energy $E$. If at an instant it is at one of extreme positions, then its linear momentum after a phase shift of $\frac{\pi}{3} \,rad$ will be
The potential energy of a particle of mass $100 \,g$ moving along $x$-axis is given by $U=5 x(x-4)$, where $x$ is in metre. The period of oscillation is .................
A mass hangs from a spring and oscillates vertically. The top end of the spring is attached to the top of a box, and the box is placed on a scale, as shown in the figure. The reading on the scale is largest when the mass is
Time period of a simple pendulum is $T$. The time taken to complete $5 / 8$ oscillations starting from mean position is $\frac{\alpha}{\beta} T$. The value of $\alpha$ is ..... .