Periodic Motion & Simple Harmonic Oscillations Explained | Chapter 14 of University Physics
Periodic Motion & Simple Harmonic Oscillations Explained | Chapter 14 of University Physics Chapter 14 delves into periodic motion and simple harmonic motion (SHM), covering how restoring forces produce oscillations, the mathematical models for springs and pendulums, energy exchange in oscillators, and the effects of damping and driving forces. Watch the full video summary here for step-by-step derivations and examples. Describing Periodic Motion Periodic motion repeats in cycles, characterized by: Amplitude (A): Maximum displacement from equilibrium Period (T): Time for one complete cycle Frequency (f): Cycles per second (Hz), f = 1/T Angular frequency (ω): 2πf Simple Harmonic Motion SHM arises when a restoring force is proportional to displacement, as in Hooke’s Law: F = –k x The solutions for motion are sinusoidal: x(t) = A cos(ωt + φ) v(t) = –ω A sin(ωt + φ) a(t) = –ω² x(t) Where ω = √(k/m) , giving the period and frequency independe...