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Frequency and Period of SHM

AP Physics 1· difficulty 4/5

A simple pendulum has period 2.0 s2.0\,\text{s} on Earth where g=9.8 m/s2g = 9.8\,\text{m/s}^2. What would its period be on the Moon where gmoon=1.62 m/s2g_{\text{moon}} = 1.62\,\text{m/s}^2 (same length)?

  • A

    approximately 2.0 s2.0\,\text{s}

  • B

    approximately 4.92 s4.92\,\text{s}

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  • C

    approximately 12.1 s12.1\,\text{s}

  • D

    approximately 1.0 s1.0\,\text{s}

Explanation

Period T∝1/gT \propto 1/\sqrt{g}, so Tmoon/TEarth=gE/gM=9.8/1.62≈2.46T_{\text{moon}}/T_{\text{Earth}} = \sqrt{g_E/g_M} = \sqrt{9.8/1.62} \approx 2.46. Thus Tmoon≈2.0⋅2.46≈4.92 sT_{\text{moon}} \approx 2.0 \cdot 2.46 \approx 4.92\,\text{s}.

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