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AP EAMCET202319 May 2023Morning ShiftPhysicsOscillationsActual

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

Options

  1. A27 ~s
  2. B4 ~s
  3. C13 ~s
  4. D7 ~s

Correct answer

D. 7 ~s

Step-by-step solution

Amplitude A=A₀ e^ -k t From given condition, A₀ 2 =A₀ e^ -0.1 t aligned & 2=0.1 t & t= 2 0.1 = 0.693 0.10 =6.935 7 ~s aligned

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