gen-define-simple-harmonic-motion-and-give-one-short-worked-exam-5835

Define simple harmonic motion and give one short worked example.

# Simple Harmonic Motion **Simple Harmonic Motion (SHM)** is oscillatory motion where the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction: **F = -kx** where k is a constant and x is displacement. This produces sinusoidal motion described by: - **Position**: x(t) = A cos(ωt + φ) - **Period**: T = 2π/ω - **Frequency**: f = 1/T --- ## Worked Example: Mass on a Spring **Problem**: A 0.5 kg mass attached to a spring oscillates with a period of 2.0 s. If the amplitude is 0.10 m, find: (a) the spring constant (b) the maximum speed **Solution**: (a) Using T = 2π√(m/k): 2.0 = 2π√(0.5/k) k = (2π)²(0.5)/(2.0)² = **4.9 N/m** (b) Maximum speed occurs at equilibrium where v_max = ωA: ω = 2π/T = 2π/2.0 = π rad/s v_max = πA = π(0.10) = **0.31 m/s**