Consider a spring mass simple harmonic oscillator in one dimension. The mass of the particle is m kg and the spring constant is k Nm⁻¹. At a given instant, the extension of the spring is x meter and t

Question

Consider a spring mass simple harmonic oscillator in one dimension. The mass of the particle is m kg and the spring constant is k Nm⁻¹. At a given instant, the extension of the spring is x meter and the speed of the particle is v ms⁻¹. On the x-v plane, if the graph of v as a function of x is a circ

Accepted Answer

Answer: k = m — In a spring mass system, the total energy is E = 1/2 mv² + 1/2 kx² or mv²/2E + kx²/2E = 1 or v²/(2E/m) + x²/(2E/k) = 1 Compare with x²/a² + y²/b² = 1 For circle a² = b² ⇒ 2E/m = 2E/k ⇒ m = k

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