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

Here,
Amplitude ( A ) = 5 cm
Time period ( T) = 0.2 sec

(a) when displacement ( x) is 5 cm
Then,
a = -w²x
= -(2π/T)²x
= - (2π/0.2)² × 5 × 10^-2
= -5π² m/s
Velocity = w√(A² - x²)
= (2π/T)√(A² - x²)
= (2π/0.2)√(0.05² - 0.05²)
= 0

(b) when x = 3 cm ,
acceleration = -w²x
= ( 2π/0.2)² × 3 × 10^-2
= (10π)² × 3 × 10^-2
= 3π² m/s

Velocity = w√(A² - x²)
= (2π/0.2)√(0.05²-0.03²)
= 0.4π² m/s

(c) when displacement is x = 0
Acceleration a = - w²x = 0
Velocity = w√(A² - x²) = wA
= (2π/0.2)√0.05²
= 0.5π m/s