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Question

The equation of motion of a body of mass 20 kg in S.H.M. is y=0.04sin(100t+π4). Then
i) Amplitude is 0.04 m
ii) Frequency is 15.92 Hz.
iii) Initial phase ϕ=π4 radians.
iv) Vmax=4ms1.
v) amax=400ms2.
vi) Max. k.E = 160 J

A
1,2 and 3 are correct
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B
1,3 and 4 are correct
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C
All are correct
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D
1, 2 3 and 5 are correct
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Solution

The correct option is C All are correct
Compare the above equation with standard equation y=Asin(ωt+ϕ)

i) Amplitude A = 0.04m
ii) Frequency ω2π=1002π=1006.28=15.92Hz.
iii) Initial phase ϕ=π4 radians.
iv) Vmax=ωA=100×0.04=4ms1.
v) amax=ω2A=1002×0.04=400ms2.
vi) Max. k.E = 12 m (Vmax)2=12×20×4×4=160J.

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