Q131 / 160 · AP EAMCET 2024 (21 May Shift 2) · Physics

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 Figure

  • A
    1s
  • B
    3.14s
  • Correct answer
    C
    1.414s
  • D
    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, $T=2 \pi \sqrt{\frac{\mathrm{~m}}{K_e}}=2 \pi \sqrt{\frac{3}{\frac{2 \times 9 \pi^2}{3}}}=\frac{6}{\sqrt{2 \times 9 \pi}}$ $=\sqrt{2}=1.414 \mathrm{~s}$

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

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