Simple Harmonic Motion Physics Example 3

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

Example 3

medium
A 0.3 kg0.3 \text{ kg} mass on a spring oscillates with amplitude 0.1 m0.1 \text{ m} and period 0.8 s0.8 \text{ s}. What is the maximum speed of the mass?

Solution

  1. 1
    Angular frequency: ω=2πT=2π0.8=7.85 rad/s\omega = \frac{2\pi}{T} = \frac{2\pi}{0.8} = 7.85 \text{ rad/s}.
  2. 2
    Maximum speed in SHM occurs at the equilibrium position: vmax⁡=ωA=7.85×0.1=0.785 m/sv_{\max} = \omega A = 7.85 \times 0.1 = 0.785 \text{ m/s}

Answer

vmax⁡≈0.785 m/sv_{\max} \approx 0.785 \text{ m/s}
In simple harmonic motion, the maximum speed occurs as the object passes through equilibrium, where all energy is kinetic. At the extremes of oscillation, the speed is zero and all energy is potential.

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 →

More Simple Harmonic Motion Examples

Example 1 easy

A mass-spring system has a spring constant [formula] and mass [formula]. What is the period of oscil

Example 2 medium

A simple pendulum has a length of [formula]. What is its period on Earth ([formula]) and on the Moon

Example 4 hard

A [formula] mass on a spring ([formula]) oscillates with amplitude [formula]. What is the total ener

← All Simple Harmonic Motion Examples Simple Harmonic Motion Concept