Simple Harmonic Motion

A rectangular block of mass m and area of cross-section A floats in a liquid of density ρ. If it is given a small vertical displacement from equilibrium, it undergoes oscillation with a time period T. Then:
1. $T\propto \sqrt{\rho }$
2. $T\propto \frac{1}{\sqrt{A}}$
3. $T\propto \frac{1}{\rho }$
4. $T\propto \frac{1}{\sqrt{m}}$

A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is:
1. $\frac{\mathrm{T}}{4}$
2. $\frac{\mathrm{T}}{8}$
3. $\frac{\mathrm{T}}{12}$
4. $\frac{\mathrm{T}}{2}$

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is:
1. 0.5$\mathrm{\backslash pi}$
2. $\mathrm{\backslash pi}$
3. 0.707$\mathrm{\backslash pi}$
4. zero

Two points are located at a distance of m and m from the source of oscillation. The period of oscillation is s and the velocity of the wave is m/s. What is the phase difference between the oscillations of two points?
1.
2.
3.
4.

The displacement of a particle along the x-axis is given by, x = asin²$\mathrm{\backslash omega}$t. The motion of the particle corresponds to:

The damping force of an oscillator is directly proportional to the velocity. The units of the constant of proportionality are:
1. kg-msec^-1
2. kg-msec^-2
3. kg-sec^-1
4. kg-sec

A particle is executing a simple harmonic motion. Its maximum acceleration is and maximum velocity is Then its time period of vibration will be:
1.
2.
3.
4.

A particle executes linear simple harmonic motion with amplitude of . When the particle is at from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:
1.
2.
3.
4.

The average velocity of a particle executing SHM in one complete vibration is:
1. zero
2.
3.
4.