Simple Harmonic Motion Physics Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

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A simple pendulum has a length of 1ย m1 \text{ m}. What is its period on Earth (g=9.8ย m/s2g = 9.8 \text{ m/s}^2) and on the Moon (g=1.6ย m/s2g = 1.6 \text{ m/s}^2)?

Solution

  1. 1
    Period of a simple pendulum: T=2ฯ€LgT = 2\pi\sqrt{\frac{L}{g}}.
  2. 2
    On Earth: TE=2ฯ€19.8=2ฯ€0.102=2ฯ€ร—0.319โ‰ˆ2.01ย sT_E = 2\pi\sqrt{\frac{1}{9.8}} = 2\pi\sqrt{0.102} = 2\pi \times 0.319 \approx 2.01 \text{ s}.
  3. 3
    On the Moon: TM=2ฯ€11.6=2ฯ€0.625=2ฯ€ร—0.791โ‰ˆ4.97ย sT_M = 2\pi\sqrt{\frac{1}{1.6}} = 2\pi\sqrt{0.625} = 2\pi \times 0.791 \approx 4.97 \text{ s}.

Answer

TEarthโ‰ˆ2.01ย s,TMoonโ‰ˆ4.97ย sT_{\text{Earth}} \approx 2.01 \text{ s}, \quad T_{\text{Moon}} \approx 4.97 \text{ s}
A pendulum swings more slowly where gravity is weaker because the restoring force is smaller. The period depends on length and gravitational acceleration, but not on mass or amplitude (for small angles).

About Simple Harmonic Motion

Oscillatory motion where the restoring force is proportional to displacement from equilibrium, producing sinusoidal position over time.

Learn more about Simple Harmonic Motion โ†’

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