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Question

The angular velocities of three bodies in simple harmonic motion are ω1,ω2,ω3 with their respective amplitudes as A1,A2,A3. If all the three bodies have same mass and velocity, the.

A
A21ω21=A22ω22=A23ω2
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B
A21ω1=A22ω2=A23ω3
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C
A1ω21=A2ω22=A3ω23
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D
A1ω1=A2ω2=A3ω3
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Solution

The correct option is D A1ω1=A2ω2=A3ω3
Rate of change of displacement is known as velocity. The equation for displacement (y) of a body in SHM with angular velocity ω is given by
y=asinωt
where a is amplitude
velocity v= rate of change of displacement =dydt
v=dydt=ddt(asinωt)=aωcosωt
Given, v1=v2=v3 and a1=A1,a2=A2.
a2=A3
A1ω1=A2ω2=A3ω3.

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