Q74 / 90 · JEE Main 2014 (11 Apr Online) · Physics

The angular frequency of the damped oscillator is given by, $\omega=\sqrt{\left(\frac{\mathrm{k}}{\mathrm{m}}-\frac{\mathrm{r}^2}{4 \mathrm{~m}^2}\right)}$ where $\mathrm{k}$ is the spring constant, $\mathrm{m}$ is the mass of the oscillator and $r$ is the damping constant. If the ratio $\frac{r^2}{\mathrm{mk}}$ is $8 \%$, the change in time period compared to the undamped oscillator is approximately as follows:

  • Correct answer
    A
    increases by $1 \%$
  • B
    increases by $8 \%$
  • C
    decreases by $1 \%$
  • D
    decreases by $8 \%$

Solution

The change in time period compared to the undamped oscillator increases by $1 \%$.

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

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