If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \mathrm{m}$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are
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The time period of simple harmonic motion of mass $\mathrm{M}$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5 K}}$, where the value of $\alpha$ is____.
Two particles executing $S.H.M.$ of same frequency, meet at $x=+A / 2$, while moving in opposite directions. Phase difference between the particles is .........
Two pendulums begins to swing simultaneously. The first pendulum makes $11$ full oscillations when the other makes $9$. The ratio of length of the two pendulums is
A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; $x = {a_1}\,\cos \,\omega t$ and $y = {a_2}\,\cos \,2\,\omega t$ traces a curve given by
The bob of simple pendulum having length $l$, is displaced from mean position to an angular position $\theta$ with respect to vertical. If it is released, then velocity of bob at lowest position
A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs of equal spring constants $k$. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $\theta$ in one direction and released. The frequency of oscillation is
Two simple pendulum first of bob mass $M_1$ and length $L_1$ second of bob mass $M_2$ and length $L_2$. $M_1 = M_2$ and $L_1 = 2L_2$. If these vibrational energy of both is same. Then which is correct