Basic Concepts and Effects

• Basic concepts: Periodic vibrations/oscillations (when do they happen?); Displacement, amplitude A, period, frequency (f = 1/T) and phase frequency ; Simple harmonic oscillator.
• Damped oscillations: Concept; Underdamped and overdamped oscillations.
• Forced oscillations: Concept; Natural frequency and resonance.

Object Attached to a Spring

• Force: Hooke's law, F = –kx.
• Mechanical energy: At an arbitrary point, E = KE + PE = mv² + kx² ; Be able to relate E to the amplitude A and to the v_max using the fact that E is conserved.
• Period: T = 2 (m/k)^1/2.
• Position as a function of time: A sinusoidal function; The most common forms are

x(t) = A cos(t)  and  A sin(t) .

Simple Pendulum

• Restoring force: Related to the angle by F = –mg sin; When can the motion of a simple pendulum be considered simple harmonic motion?
• Period: T = 2 (L/g)^1/2.