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Q.

A particle in S.H.M. is described by the displacement function x(t) = a cos (ωt + θ).If the initial (t = 0) position of the particle is I cm and its initial velocity is π cm/s. The angular frequency of the particle is π rad/s, then its 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 = a cos (ωt + θ)------------(i)And v = dxdt = -aω sin(ωt+θ)--------(ii)Given at t = 0, x = 1 cm and v = π and ω = πPutting these values in equation (i) and (ii), we will getsin θ = -1a and cos θ = 1A⇒ sin2θ + cos2θ = (-1a)2+(1a)2 ⇒ a = 2 cm

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