Question

a body describes simple harmonic motion with amplitude of 5cm and a period of 0.2sec.Find the acceleration and velocity of the body when the displacement is 3cm?​

Answer 1

Answer:

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

Explanation:

A = 5 cm = 0.05 m

T = 0.2 s

ω=2π/T=2π/0.2=10πrad/s

When displacement is y, then acceleration, a=−ω

2

y

Velocity, V=ω

r

2

−y

2

Case (a) When y=5cm=0.05m

a=−(10π)

2

×0.05=−5π

2

m/s

2

V=10π×

(0.05)

2

−(0.05)

2

=0

Case (b) When y=3cm=0.03m

a=−(10π)

2

×0.03=−3π

2

m/s

2

V=10π×

(0.05)

2

−(0.03)

2

=10π×0.04=0.4π m/s

Case (c) When y=0

a=−(10π)

2

×0=0

V=10π×

(0.05)

2

−0

2

=10π×0.05=0.5πm/s

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