The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176 rad/s. The frequency of

Question

The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176 rad/s. The frequency of this simple harmonic oscillator is Hz. [Take = 227]

Accepted Answer

Given: The angular frequency of kinetic energy oscillation is $\omega_{KE} = 176 \, \text{rad/s}$ .

Find: The frequency of the simple harmonic oscillator.

In a simple harmonic oscillator with displacement $x(t) = A \sin(\omega t + \phi)$ , the kinetic energy depends on the square of velocity. Therefore, the kinetic energy oscillates with twice the angular frequency of the oscillator.

\omega_{KE} = 2\omega_{SHO}

So,

2\omega_{SHO} = 176

\omega_{SHO} = \frac{176}{2} = 88 \, \text{rad/s}

Now use the relation between angular frequency and linear frequency:

f = \frac{\omega}{2\pi}

Thus,

f_{SHO} = \frac{88}{2\pi} = \frac{88}{2 \cdot \frac{22}{7}}

f_{SHO} = \frac{88 \times 7}{44} = 14 \, \text{Hz}

Therefore, the frequency of the simple harmonic oscillator is $14 \, \text{Hz}$ . The correct option is C.

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