The displacement of a damped harmonic oscillator is given by x t = e - 0.1 t cos ⁡ 10 π t + φ . Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value

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The displacement of a damped harmonic oscillator is given by x t = e - 0.1 t cos ⁡ 10 π t + φ . Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to:

TestHub · Accepted Answer

Amplitude A = A 0 e - k t From given condition, A 0 2 = A 0 e - 0.1 × t ⇒ l n 2 = 0.1 × t t = l n 2 0.1 = 0.693 0.10 = 6.935 ≈ 7 s

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