Some Systems Executing Simple Harmonic Motion

If the maximum velocity and acceleration of a particle executing SHM are equal in magnitude, the time period will be ______.

Answer the following questions:

What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?

The phase difference between displacement and acceleration of a particle performing S.H.M. is _______.

(A) `pi/2rad`

(B) π rad

(C) 2π rad

(D)`(3pi)/2rad`

Show that motion of bob of the pendulum with small amplitude is linear S.H.M. Hence obtain an expression for its period. What are the factors on which its period depends?

A cylindrical log of wood of height h and area of cross-section A floats in water. It is pressed and then released. Show that the log would execute S.H.M. with a time period. `T = 2πsqrt(m/(Apg))` where m is mass of the body and ρ is density of the liquid.

The relation between acceleration and displacement of four particles are given below: Which one of the particles is executing simple harmonic motion?

A particle executing S.H.M. has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s². The period of oscillation is ______.

The acceleration due to gravity on the surface of moon is 1.7 ms^–2. What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s? (g on the surface of earth is 9.8 ms^–2)