Question

A body describes simple harmonic motion with amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is (a) 5 cm, (b) 3 cm, (c) 0 cm.

Answer 1

Amplitude, A = 5 cm = 0.05 m

Time period, T = 0.2 s

(a) For displacement, x = 5 cm = 0.05 m

Acceleration is given by:

a = –

Velocity is given by:

v

= 0

When the displacement of the body is 5 cm, its acceleration is
–5π² m/s² and velocity is 0.

(b) For displacement, x = 3 cm = 0.03 m

Acceleration is given by:

a =

Velocity is given by:

v

= 0.4 π m/s

When the displacement of the body is 3 cm, its acceleration is –3π m/s² and velocity is 0.4π m/s.

(c) For displacement, x = 0

Acceleration is given by:

a = 0

Velocity is given by:

When the displacement of the body is 0, its acceleration is 0 and velocity is 0.5 π m/s.