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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 , where t is the time in seconds. The time taken for the amplitude of the oscillator to drop to half of its initial value is close to

Options

  1. A13   s
  2. B7 s
  3. C4 s
  4. D27 s

Correct answer

B. 7 s

Step-by-step solution

A 0 2 = A 0 e - 0 . 1 t ⇒ e - 0 . 1 t = 2 ⇒ 0 . 1 t = l n 2 t = ℓn 2 0 . 1 = 10 en 2 = 6 . 93 = 7 s

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