In a spring block system as shown in figure, if the spring constant $\mathrm{K}=9 \pi^2 \mathrm{Nm}^{-1}$,…

In a spring block system as shown in figure, if the spring constant $\mathrm{K}=9 \pi^2 \mathrm{Nm}^{-1}$, then the time period of oscillation is
  1. 1s
  2. 3.14s
  3. 1.414s
  4. 0.5s

Solution

$\mathrm{K}_{\mathrm{e}}=\frac{(2 \mathrm{k})(\mathrm{k})}{2 \mathrm{k}+\mathrm{k}}=\frac{2 \mathrm{k}}{3}$ $\therefore$ Time period, $T=2 \pi \sqrt{\frac{\mathrm{~m}}{K_e}}=2 \pi \sqrt{\frac{3}{\frac{2 \times 9 \pi^2}{3}}}=\frac{6}{\sqrt{2 \times 9 \pi}}$ $=\sqrt{2}=1.414 \mathrm{~s}$

Asked in: AP EAMCET 2024 (21 May Shift 2)

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