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Classical Mechanics

Forces, motion, energy, and the laws that govern how things move.

Lessons

All lessons

Lagrangian Dynamics: Minimizing Action in Constrained Systems

Master the Euler-Lagrange equations to derive complex equations of motion for constrained mechanical systems.

Principles of Angular Momentum: The Gyroscopic Effect

Explore how angular momentum conservation governs the stability of rotating systems.

Challenges

Variable-Damping Harmonic Oscillator Array

Design and construct a multi-stage mechanical oscillator system that exhibits a non-linear decay profile under varying damping coefficients. You must engineer a mechanism that allows for the real-time adjustment of energy dissipation rates without altering the fundamental frequency of the primary oscillating mass. The performance will be evaluated based on the precision of the achieved damping ratio compared to a predefined logarithmic decrement curve.