Question

13. A particle starts SHM from the mean position. Its amplitude is A and its time period T. at one
time its speed is half that of the maximum aped. What is this displacement,
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Answer 1

Answer:

A particle starts S.H.M. from the mean position. Its amplitude is A and time period is T . At the time when its speed is half of the maximum speed, its displacement y is :

The relation between angular frequency and displacement is given as

v=ω

A

2

−x

2

Suppose

x=Asinωt

On differentiating the above equation w.r.t. time we get

dt

dx

=Aωcosωt

The maximum value of velocity will be\[{v_{\max }} = A\omega \]

The displacement for the time when speed is half the maximum is given as

v=

2

Aω

A

2

ω

2

=4ω(A

2

−x

2

)

By substituting the value in(1)we get the displacement as

x=

2

A

3