The amplitude of oscillation of a pendulum is 5 cm and the period is 2 s. Find the maximum speed — Physics problems | PhysLabo
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Maximum speed of a pendulum

Medium 11 grade Oscillations / Mechanical Oscillations

The amplitude of oscillation of a simple pendulum is $A = 5$ cm and the period is $T = 2$ s. Find the maximum speed of the pendulum.

Given
  • $A = 5$ cm $= 0.05$ m
  • $T = 2$ s
  • $v_{\text{max}} = ?$
Visual demonstration
Hints
Hint 1 / 2
The maximum speed of an oscillation is $v = A\omega$.
Hint 2 / 2
$\omega = 2\pi/T$, and convert the amplitude to metres: $5$ cm $= 0.05$ m.
Solution

The maximum speed is reached at the equilibrium position and equals $v_{\text{max}} = A\omega$, where $\omega = 2\pi/T$:

$$v_{\text{max}} = A \cdot \frac{2\pi}{T} = 0.05 \cdot \frac{2\pi}{2} = 0.05\pi \approx 0.157 \text{ m/s}$$

Answer

$v_{\text{max}} \approx 0.157$ m/s