Simple Harmonic Motion - Mechanics - Physics Previous Year Questions

A piston is performing S.H.M. in the vertical direction with a frequency of \(0.5 \mathrm{~Hz}\). A block of \(10 \mathrm{~kg}\) is placed on the piston. The maximum amplitude of the system such that the block remains in contact with the piston is

A tray of mass \(12 \mathrm{~kg}\) is supported by two identical springs as shown in figure. When the tray is pressed down slightly and then released, it executes SHM with a time period of \(1.5 \mathrm{~s}\). The spring constant of each spring is

A pendulum oscillates simple harmonically and only if

I. the sizer of the bob of pendulum is negligible in comparison with the length of the pendulum.

II. the angular amplitude is less than \(10^{\circ}\).

Choose the correct option.

The displacement of a particle executing SHM is given by \(x=3 \sin \left[2 \pi t+\frac{\pi}{4}\right]\), where \(x\) is in metre and \(t\) is in seconds. The amplitude and maximum speed of the particles is

A block of mass \(m\) is connected to a light spring of force constant \(k\). The system is placed inside a damping medium of damping constant \(b\). The instantaneous values of displacement, acceleration and energy of the block are \(x, a\) and \(E\) respectively. The initial amplitude of oscillation is \(A\) and \(\omega^{\prime}\) is the angular frequency of oscillations. The incorrect expression related to the damped oscillations is

For a particle executing simple harmonic motion (SHM), at its mean position

The variations of kinetic energy $K(x)$, potential energy $U(x)$ and total energy as a function of displacement of a particle in SHM is as shown in the figure. The value of $\left|x_0\right|$ is