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A rod of mass $m$ and length $l$ is suspended from ceiling with two string of length $l$ as shown. When the rod is given a small push in the plane of page and released time period is $T_1$ and when the rod is given a push perpendicular to plane time period of oscillation is $T_2$ . The ratio $\frac{{T_1^2}}{{T_2^2}}$ is
A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration $a$, then the time period is given by $T = 2\pi \sqrt {\frac{l}{{g'}}} $, where $g'$ is equal to
The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended, the period of oscillation will now be
Two particles are executing $SHM$ in a straight line. Amplitude $'A'$ and time period $'T'$ of both the particles are equal. At time $t = 0$ one particle is at displacement $x_1 = +A$ and other at ${x_2} = \frac{{ - A}}{2}$ and they are approaching towards each other. Time after which they will cross each other is
A pendulum bob has a speed of $3\, m/s$ at its lowest position. The pendulum is $0.5\, m$ long. The speed of the bob, when the length makes an angle of ${60^o}$ to the vertical, will be ..... $m/s$ (If $g = 10\,m/{s^2}$)
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is $10\,s^{-1}$. At, $t = 0$ the displacement is $5\, m$. What is the maximum acceleration ? The initial phase is $\frac{\pi }{4}$
A $2\, Kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi ^2 N/m$ attached to $2\, Kg$ block at rest kept on a smooth floor. The time for which rear moving block remain in contact with spring will be ... $\sec$