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") = 20 pi`
What is the frequency of the simple harmonic motion?

Options

A. 100 Hz
B. 20 Hz
C. 10 Hz
D. `1/10 Hz`

Answer

C

Explanation

As the resultant curve is ellipse then equation for S.H.M. is

`v^(2)/(OQ)^(2) + x^(2)/(OP)^(2) =1`…………..(i)
Now, `OQ = aomega [therefore v = romega = aomega]` and OP =a, where `omega` = angular velocity
From eqn. (i) `v^(2)/(a^(2)omega^(2)) + x^(2)/a^(2) =1`
Thus, major axis, `=2 xx aomega = 2aomega`, minor axis = 2a
Given, that `("major axis along X")/("minor axis along Y") = 20pi, therefore (2aomega)/(2a) = 20pi`
`f= 10Hz`