Oscillations
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Question : 24
Total: 25
A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of body when the displacement is (a) 5 cm, (b) 3 cm and (c) 0 cm.
Solution:
Here,r = 5 c m = 0.05 m T = 0.2 s ω =
=
= 10 π rad s − 1
When displacement is y, then acceleration,a = − ω 2 y
velocity,v = ω √ r 2 − y 2
Case (a) When y = 5 cm = 0.05 m
a = − ( 10 π ) 2 × 0.05 = − 5 π 2 m s − 2 ,
v = 10 π √ ( 0.05 ) 2 − ( 0.05 ) 2 = 0
Case (b) When y = 3 cm = 0.03 m
a = − ( 10 π ) 2 × 0.03 = − 3 π 2 m s − 2 ,
v = 10 π √ ( 0.05 ) 2 − ( 0.03 ) 2 = 10 π × 0.04 = 0.4 π m s − 1
Case (c) When y = 0
a = − ( 10 π ) 2 × 0 = 0 ,
v = 10 π √ ( 0.05 ) 2 − ( 0 ) 2 = 10 π × 0.05 = 0.5 π m s − 1
When displacement is y, then acceleration,
velocity,
Case (a) When y = 5 cm = 0.05 m
Case (b) When y = 3 cm = 0.03 m
Case (c) When y = 0
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