SHM occurs when a restoring force is proportional to displacement from equilibrium (F = -kx for springs, F = -mgsin(theta) approximated as -mgtheta for small-angle pendulums). Period depends on system properties, not amplitude. Energy oscillates between kinetic and potential. SHM connects directly to Big Ideas 4 and 5 through energy conservation.
- Restoring force: A force directed back toward equilibrium, proportional to displacement: F = -kx.
- Period of a mass-spring system: T = 2pisqrt(m/k); depends on mass and spring constant, not amplitude.
- Period of a simple pendulum: T = 2pisqrt(L/g); depends on length and gravitational field strength, not mass or amplitude (for small angles).
- Energy in SHM: Total mechanical energy E = 1/2 kA^2 is constant; KE is maximum at equilibrium, PE is maximum at maximum displacement.
Can you predict how the period of a pendulum changes if you double its length, move it to the Moon, or double the mass of the bob?
| Change | Effect on period of mass-spring | Effect on period of pendulum |
|---|
| Double the mass | Increases by factor of sqrt(2) | No change |
| Double the spring constant / halve the length | Decreases by factor of sqrt(2) | Decreases by factor of sqrt(2) |
| Move to Moon (g decreases) | No change | Increases (longer period) |
| Double the amplitude | No change | No change |