The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176 rad/s. The frequency of this simple harmonic oscillator i $s_____Hz.$ [take π = 22/7]
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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 i s_____Hz. [take π = 22/7]

G1 Physics · Accepted Answer

If the displacement in SHM is x = A cos(ωt + φ), then the kinetic energy varies as K ∝ sin²(ωt + φ). Because sin²θ has angular frequency 2ω, the angular frequency of kinetic-energy oscillation is ω(KE) = 2ω. Given, ω(KE) = 176 rad/s. Therefore, ω = 88 rad/s. The frequency of the simple harmonic oscillator is f = ω/(2π). Using π = 22/7, f = 88/[2(22/7)] = 88 × 7/44 = 14 Hz. Correct option: A.