Simple Harmonic Motion Notes

Simple Harmonic Motion

  • Periodic motion resembling a sine function: y=sin(x)y = sin(x)

Causes of Simple Harmonic Motion

  • Restoring force directly proportional to displacement (e.g., Hooke's Law).

Hooke's Law

  • Applies primarily to springs.
  • Restoring Force: F=−kxF = -kx
    • The negative sign indicates that the force works in the opposite direction of the displacement.

Conservation of Energy in Springs

  • Total energy (KE + PE) remains constant, neglecting dissipation.

Springs, Waves, and Circles

  • Amplitude (A) of a wave is analogous to displacement (x) of a spring (measured in meters).
  • Period (T): Time for one complete oscillation/cycle (seconds).
  • Frequency (f): f=1/Tf = 1/T (Hertz).
  • Angular Frequency ($\omega$): ω=2πf=2πT\omega = 2\pi f = \frac{2\pi}{T}

Mass-Spring Systems

  • Vertical systems (under gravity) are treated similarly to horizontal systems; gravity only changes the equilibrium position.