A simple pendulum, consisting of a small ball of mass m attached to a massless string hanging vertically from the ceiling is oscillating with an amplitude such that T_max = 2T_min, where T_max and T_min are the maximum and minimum tension in the string, respectively. The value of maximum tension T_max in the string is

The bob of a swinging second pendulum (one whose time period is 2 s) has a small speed v₀ at its lowest point. It height from this lowest point 2.25 s after passing through it, is given by

In case of a simple harmonic motion, if the velocity is plotted along the X-axis and the displacement (from the equilibrium position) is plotted along the Y-axis, the resultant curve happens to be an ellipse with the ratio $${{major\,axis\,(along\,X)} \over {minor\,axis\,(along\,Y)}} = 20\pi $$

What is the frequency of the simple harmonic motion?

The velocity of a particle executing a simple harmonic motion is 13 ms^$$-$$1, when its distance from the equilibrium position (Q) is 3 m and its velocity is 12 ms^$$-$$1, when it is 5 m away from Q. The frequency of the simple harmonic motion is