Week 4 Forced Damped Harmonic Motion & Coupled Oscillators Flashcards
what 3 things can be observed from the Power resonance curve
> if there is no damping there is no dissipation of energy
for steady state oscillations the total power delivered to the oscillator over each complete cycle is 0
for damped oscillations the driving force sustains the oscillations so the power absorbed by the oscillator is equal to the rate of energy dissipation
what is the instantaneous power equation
P(t) = bv(t) * v(t)
what does the power resonance curve tell us
how the average power absorbed per cycle changes with driving frequency
what defines the sharpness of resonance
width of the power resonance curve around resonant frequency
what is the power resonance Q equation
Q = ω0 / ωfwhh
what are the two conditions required to solve a second ODE
> the complementary function of the ODE is homogeneous f(x) = 0
the sum of the CF and PI is inhomogeneous f(x) =/ 0
what are the 3 steps to find the CF
> find the auxiliary equation
find the solutions of the auxiliary equation
use the auxiliary solutions to find the CF solution
what are the two normal modes for a general coupled pendula system
1) displace each pendulum by the same amount in the same direction so that they oscillate in phase with same frequency
2) displace each pendulum by same amount in opposite directions so they oscillate out of phase and with different frequency
what are the two normal frequencies for a coupled pendula system
ω1^2 = g/l ω2^2 = g/l + 2k/m
