Last Minute Lecture

Inductance & Circuit Oscillations Explained | Chapter 30 of University Physics Chapter 30 introduces the concept of inductance—how changing currents and magnetic fields interact to store energy—and examines the dynamic behavior of RL, LC, and LRC circuits. You’ll see how mutual and self-inductance drive real-world applications from smoothing filters to oscillators. Watch the full video summary here for step-by-step derivations and demonstrations. Mutual Inductance When the current in one coil changes, it induces an emf in a nearby coil. This mutual inductance M depends on coil geometry and core material: Emf induced in coil 2: ℰ₂ = –M·(di₁/dt) Emf induced in coil 1: ℰ₁ = –M·(di₂/dt) Definition: M = (N₂·Φ₂)/i₁ = (N₁·Φ₁)/i₂ Self-Inductance & Inductors A changing current in a coil induces an emf in itself, characterized by the self-inductance L: ℰ = –L·(di/dt) L = N·Φ/i , where N is the turn count and Φ the magnetic flux per turn Inductors resis...

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...