Simple Harmonic...

A small sphere carrying a charge ‘q’ is hanging in between two parallel plates by a string of length L. Time period of pendulum is T₀. When parallel plates are charged, the electric field between the plates is E and time period changes to T. The ratio T/T₀ is equal to 

A simple pendulum has a time period T₁ when on the earth’s surface and T₂ when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of T₂/T₁ is:

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

When two displacements represented by y₁=asin(ωt) and y₂=bcos(ωt) are superimposed,the motion is -

The displacement of a particle along the r-axis is given by x = asin²ωt,t. The motion of the particle corresponds 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

A body performs simple harmonic motion about x=0 with an amplitude a and a time period T. The speed of the body at x = a/2 will be:

Which one of the following equations of motion represents simple harmonic motion?

where k, k₀, k₁ and αα are all positive.

Two simple harmonic motions of angular frequency 100 rad s ^-1 and 1000 rad s⁻¹ have the same displacement amplitude. The ratio of their maximum acceleration will be

A point performs simple harmonic oscillation of period T and the equation of motion is given by x= a sin (ωt +π/6). After the elapse of what fraction of the time period the velocity of the point will be equal to half to its maximum velocity?