Question

Starting from the origin, a body oscillates simple harmonically with an amplitude of 2m and a period of 2s.

1. What do you mean simple harmonic motion.

2. Draw the variation of displacement with time for the above motion.

3. After what time, will its kinetic energy be 75% of the total energy?

Answer 1

1. The oscillatory motion is said to be simple harmonic motion if the displacement ‘x’ of the particle from the origin varies with time as

X(t) = A cos (ωt + Φ)

where

x(t) = displacement x as a function of time t

A = amplitude

ω = angular frequency

(ω t + Φ) = phase (time-dependent)

Φ = phase constant or initial phase

2.

3. 

y = a sin ω t

ν = aω cos ωt

Kinetic energy,