Oscillations Flashcards
Rate of oscillation of KE and PE in an oscillator
Have double the angular frequency of displacement.
Trigonometric functions squared can be converted to trig functions in terms of 2theta
How to find average energy over a time period
Integrate over a time period, then divide by the time period in terms of angular frequency
Generic equation for energy in a potential energy minimum
E = KE + PE = 0.5(u)(x dot)^2 + 0.5(w)x^2
Where u and w are generic variables
When CoM can move
When there’s an external force
What can be used if CoM doesn’t move on a spring system where things pull in opposite directions
m1 * x1 = m2 * x2
Where m stands for mass and x stands for the displacement from the original position of each mass
Logarithmic decrement
2pi * gamma / omega d
Omega d
sqrt( (omega 0)^2 - (gamma)^2)
Quality factor
Number of radians an oscillation requires to fall by a factor of e
( omega 0 ) / 2gamma
For high quality oscillators: omega 0 is approximately equal to omega d.
–> Q = pi / logarithmic decrement
delta omega
The width of a normalised power against angular frequency plot of an oscillation when the power is half the maximum.
When a charged particle experiences a force in a magnetic field
When it moves in a direction that isn’t parallel to the flux
Force on a charged particle in a magnetic field
Orthogonal to both the particle’s velocity and the direction of the field
F = q ( v x B)
CROSS PRODUCT
Emf from magnetic induction
emf = - rate of change of magnetic flux
Magnetic flux
Area * Magnetic flux density
Energy stored on an inductor
0.5LI^2
Width of a power curve
2 gamma
