Simple Harmonic Motion Physics Example 4

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

Example 4

hard
A 0.5 kg0.5 \text{ kg} mass on a spring (k=200 N/mk = 200 \text{ N/m}) oscillates with amplitude 0.04 m0.04 \text{ m}. What is the total energy of the system, and what is the speed when the displacement is 0.02 m0.02 \text{ m}?

Solution

  1. 1
    Total energy equals maximum PE: E=12kA2=12(200)(0.04)2=12(200)(0.0016)=0.16 JE = \frac{1}{2}kA^2 = \frac{1}{2}(200)(0.04)^2 = \frac{1}{2}(200)(0.0016) = 0.16 \text{ J}.
  2. 2
    At x=0.02 mx = 0.02 \text{ m}: PE = 12(200)(0.02)2=0.04 J\frac{1}{2}(200)(0.02)^2 = 0.04 \text{ J}. KE = E−PE=0.16−0.04=0.12 JE - PE = 0.16 - 0.04 = 0.12 \text{ J}.
  3. 3
    Speed: v=2×KEm=0.240.5=0.48≈0.693 m/sv = \sqrt{\frac{2 \times KE}{m}} = \sqrt{\frac{0.24}{0.5}} = \sqrt{0.48} \approx 0.693 \text{ m/s}.

Answer

E=0.16 J,v≈0.693 m/sE = 0.16 \text{ J}, \quad v \approx 0.693 \text{ m/s}
In SHM, total energy is constant and continuously exchanges between kinetic and potential forms. At any displacement, the speed can be found using energy conservation.

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 3 medium

A [formula] mass on a spring oscillates with amplitude [formula] and period [formula]. What is the m

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