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Q.

A particle in S.H.M. is described by the displacement function x(t)=acos(ωt+θ) . If the initial (t=0) position of the particle is 1 cm and its initial velocity is π cm/s . The angular frequency of the particle is π rad/s, then it’s amplitude is

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a

1 cm

b

2 cm

c

2 cm

d

2.5 cm

answer is B.

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Detailed Solution

x=acos(ω t+θ) ….(i)and v=dxdt=−aωsin(ω t+θ) ….(ii)Given at t=0, x=1 cm and v=π and ω=πPutting these values in equation (i) and (ii) we will get sinθ=−1a and cosθ=1a⇒sin2θ+cos2θ=−1a2+1a2 ⇒a=2 cm

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