A spring pendulum of mass 0.5 kg and spring stiffness 50 N/m. Find the period of oscillation — Physics problems | PhysLabo
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Period of a spring pendulum

Easy 11 grade Oscillations / Mechanical Oscillations
Problem statement

A spring pendulum has a mass $m = 0.5$ kg and a spring stiffness $k = 50$ N/m. Find the period of oscillation of this pendulum.

Given
  • $m = 0.5$ kg
  • $k = 50$ N/m
  • $T = ?$
Visual demonstration
Hints
Hint 1 / 2
The period depends on the mass and the stiffness: $T = 2\pi\sqrt{m/k}$.
Hint 2 / 2
$0.5/50 = 0.01$, and the square root of $0.01$ is $0.1$.
Solution

The period of oscillation of a spring pendulum:

$$T = 2\pi \sqrt{\frac{m}{k}} = 2\pi \sqrt{\frac{0.5}{50}} = 2\pi \sqrt{0.01} = 2\pi \cdot 0.1 \approx 0.63 \text{ s}$$

Answer

$T \approx 0.63$ s

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