# Oscillations

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• Created by: cmidona
• Created on: 17-12-13 19:23
Angular frequency
ω = 2πf
1 of 22
Displacement as a function of time
x = xm cos(ωt + φ)
2 of 22
velocity as a function of time
v = -vm sin(ωt + φ)
3 of 22
Acceleration as a function of time
a = -am cos(ωt + φ)
4 of 22
Angular frequency
ω = sqrt(k/m)
5 of 22
Time period of spring with mass
T = 2π sqrt(m/k)
6 of 22
Restoring torque
τ = Iα
7 of 22
Elastic potential energy
U = 1/2 kx^2
8 of 22
Spring force and constant
F = -kx
9 of 22
Equation of motion
d^2x/dt^2 = -k/m x(t)
10 of 22
Restoring torque of a physical pendulum
τ = -hFsinθ
11 of 22
Angular equation of motion
d^2θ/dt^2 = -mgh/I θ
12 of 22
Damping force and constant
F = -bv
13 of 22
undamped
b/2m = 0
14 of 22
underdamped
b/2m < ω
15 of 22
overdamped
b/2m > ω
16 of 22
critical damping
b/2m = ω
17 of 22
Total mechanical energy
E = 1/2 kx^2
18 of 22
Quality factor
Q= 2π (energy stored in the oscillator)/(energy dissipated in one cycle
19 of 22
Quality factor for underdamped oscillator
Q = τω
20 of 22
Forced oscillations
F = F0 cost(ωt)
21 of 22
Resonance
ωres = sqrt(ω^2 - (b^2/2m^2))
22 of 22

## Other cards in this set

### Card 2

#### Front

Displacement as a function of time

#### Back

x = xm cos(ωt + φ)

### Card 3

#### Front

velocity as a function of time

### Card 4

#### Front

Acceleration as a function of time

### Card 5

#### Front

Angular frequency