Simple Harmonic Motion Flashcards
1
Q
Hooke’s Law Equation
A
F = -kx
2
Q
Simple Harmonic Equation
A
- d^2 x/dt^2 + (ω^2) x = 0
- N2 = Hooke’s Law
3
Q
Angular Frequency Equation (k,m,ω)
A
- ω^2 = k/m
- k = spring constant
- m = mass
4
Q
Simple Harmonic Motion Equation Trial Solution
A
x = A cos (λt)
x = B sin (λt)
5
Q
Simple Harmonic Motion General Solution Equation
A
x = A cos (ωt) + B sin (ωt)
6
Q
Frequency Equation
A
f = ω / 2π
7
Q
Simple Harmonic Motion Solution Equation with Phase
A
x = A cos (ωt + ϕ)
8
Q
Potential of a spring
A
- U = (1/2) k x^2
- Where potential is 0 at x=0
9
Q
What is the ratio of Potential and Kinetic Energy
A
- 50:50
- Equipartition of Energy
- <T> = <u> = (1/4) k A^2
</u></T>
10
Q
General SHM Equation Solution with Phase in exponential form
A
x = Re ( A e^i(ωt+ϕ) )
11
Q
Complex Amplitude Equation
A
a = A e ^(iϕ)
12
Q
General SHM Equation Solution with Complex Amplitude
A
x = Re (a e^(iωt) )
13
Q
Damped SHM Equation
A
- d^2 x/dt^2 + γ dx/dt + ω^2 x = 0
- γ = b/m
- b is a damping constant
14
Q
Trial Solution to Damped SHM
A
z = a e^(pt)
15
Q
Condition for light damping
A
γ < 2ω
