Q130 / 160 · TS EAMCET 2024 (09 May Shift 1) · Physics

In a time ' $t$ ', the amplitude of vibrations of a damped oscillator becomes half of its initial value, then the mechanical energy of the oscillator decreases by

  • A
    $40 \%$
  • B
    $20 \%$
  • Correct answer
    C
    $75 \%$
  • D
    $50 \%$

Solution

The variation in amplitude of damped harmonic oscillator with time $t$ is given by $A=A_0 e^{-b t}$ $\therefore \frac{\mathrm{A}_0}{2}=\mathrm{A}_0 \mathrm{e}^{-\mathrm{bt}} \therefore \mathrm{e}^{\mathrm{bt}}=\mathbf{2}$ For a damped oscillator if the damping is small then the mechanical energy decreases exponentially as $\mathrm{E}=\frac{1}{2} \mathrm{kx}^2 \mathrm{e}^{-bt}$

Hence, the correct answer is option: 'C'.

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