Oscillations practice quiz

Key ideax = A cos(ωt + φ), so v_max = Aω and a_max = Aω². Any system with d²x/dt² = −ω²x is simple harmonic.

Common mistakeMixing up ω (angular frequency) with f, or using sine where the initial conditions call for cosine.

Key ideaT = 2π/ω. For a spring, ω = √(k/m); for a physical pendulum at small angles, ω = √(mgd/I).

Common mistakeUsing the simple-pendulum formula for an extended object.

Key ideax, v and a are sinusoids: v is a quarter-cycle out of step with x, and a is half a cycle out of step (always opposite to x). v is greatest where x = 0, and a is greatest at the extremes.

Common mistakePlacing the velocity maximum at the displacement maximum.

Key ideaE = ½kA² is constant. K and U each oscillate at twice the motion’s frequency.

Common mistakeThinking K and U have the same period as the motion.

Key ideaFor small angles, a simple pendulum has T = 2π√(L/g) and a physical pendulum has T = 2π√(I/mgd).

Common mistakeUsing the simple-pendulum formula for a rod or other extended object.