Oscilation Equations

Question 1

Period Equation

Answer 1

2pi sq root (#). For Simple Pendulum, # L/g (simple pendulem). For spring, M/k (linear simple harmonic operator). For natural pendulum, I/mgh.

Torque is useful for any pendulum.

Question 2

Acceleration Equation for SHM

Answer 2

a = -w^2 x

Question 3

Angular Frequnecy

Answer 3

2pi / T, though T changes depending on system time. Effectively just #.

Question 4

Frequency Relation.

Answer 4

w = 2pi f

Question 5

Total Mech E in SHM

Answer 5

1/2k A^2 or 1/2 m Vmax^2

Question 6

SHM Definition

Answer 6

Acceleration is proportional to distance and towards equilibrium position.

Question 7

Damped Harmonic Motion

Answer 7

When external forces inhibit oscillations, turning mechanical energy to thermal. If damping force is minus some constant * v, displacement = x e^(damping force/2pi) cos (w’ t + phase), where w’ is (k/m - b^2 / 4m^2)^0.5. If constant is small, w’ = w.

Question 8

Resonance

Answer 8

When external force acts periodically on an oscillating system, translational velocity amplitude is greatest when angular frequencies are equal. Similar for position.