The mass of a particle is 1 kg and it is moving along $x$ - axis. The period of its oscillation is…

The mass of a particle is 1 kg and it is moving along $x$ - axis. The period of its oscillation is $\frac{\pi}{2}$. Its potential energy at a displacement of 0.2 m is
  1. 0.24 J
  2. 0.48 J
  3. 0.32 J
  4. 0.16 J

Solution

$\begin{aligned} & \text { }{ }^{\prime}=\frac{\pi}{2} \mathrm{~s}, \mathrm{~m}=1 \mathrm{~kg}, \mathrm{x}=0.2 \mathrm{~m} \\ & \therefore \quad \omega=\frac{2 \pi}{\mathrm{~T}}=\frac{2 \pi \times 2}{\pi}=4 \mathrm{rad} / \mathrm{s} \end{aligned}$ $\therefore \quad$ Potential energy, $\begin{aligned} & \mathrm{U}=\frac{1}{2} \mathrm{kx}^2=\frac{1}{2} \mathrm{mw}^2 \mathrm{x}^2=\frac{1}{2} \times 1 \times 4^2 \times 0.2 \times 0.2 \\ & =0.32 \mathrm{~J} \end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 1)

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