Simple Harmonic Motion
Classroom worksheet · Interactive simulation: https://lkforge.com/tools/physics/simple-harmonic-motion/
Name: Date:
Learning objectives
- Identify the restoring force behind simple harmonic motion.
- Relate period to mass and spring constant.
- Describe the exchange between kinetic and potential energy.
Variables to change
- Mass
- Spring constant
- Amplitude
Procedure
- Set a mass on a spring and measure the period.
- Increase the mass and measure the period again.
- Increase the spring constant (stiffer spring) and measure the period.
- Watch where the speed is greatest and where it is zero.
Observations
Record period versus mass and spring constant, and note where kinetic and potential energy peak.
Questions
- What provides the restoring force in a mass–spring system?
- How does increasing mass affect the period?
- How does a stiffer spring (larger k) affect the period?
- Where is the mass moving fastest? Where is it momentarily at rest?
- Does amplitude affect the period in ideal SHM?
Answer key (instructors)
- 1. The spring force, F = -kx, always directed back toward equilibrium.
- 2. The period increases; T = 2π√(m/k).
- 3. The period decreases — stiffer springs oscillate faster.
- 4. Fastest at equilibrium (maximum kinetic energy); at rest at the extremes (maximum potential energy).
- 5. No — the period is independent of amplitude for ideal simple harmonic motion.
Simple harmonic motion arises from a restoring force proportional to displacement (F = -kx). The period T = 2π√(m/k) grows with mass and shrinks with stiffness, and energy shifts continually between kinetic (at center) and potential (at the extremes).