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In case of a simple harmonic motion, if ...

In case of a simple harmonic motion, if the velocity is plotted along the X-axis and the displacement (from the equilibrium position) is plotted along the Y-axis, the resultant curve happens to be an ellipse with the ratio
`("major axis (along X)")/("minor axis (along Y)")=20pi`
What is the frequency of the simple harmonic motion?

A

100 Hz

B

20 Hz

C

10 Hz

D

`1/10` Hz

Text Solution

Verified by Experts

The correct Answer is:
C
Let, `x=Asinomegat`
`therefore" "(dx)/(dt)=Aomegacosomegat or,v=Aomegacosomegat`
`therefore" "x^(2)/A^(2)+v^(2)/((Aomega)^(2))=sin^(2)omegat+cos^(2)omegat=1`
According to the question,
`("major axis (along X)")/("minor axis (along Y)")=20pi`
or, `(2Aomega)/(2A)=20pior,omega=20pi`
or, `2pif=20pior,f=10Hz`
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