5.8 oscillations Flashcards
what is the formula for displacement in terms of time?
x = x0sin(wt + Φ) or x = x0cos(wt + Φ)
what is w and how to calculate?
angular frequency, 2πf or 2π/T
what is the defining equation of simple harmonic motion?
a = -w^2x
define simple harmonic motion
the oscillatory motion of a particle whose acceleration is directly proportional to its displacement from a fixed point and always in the opposite direction from displacement
what is the formula for velocity in terms of time?
v = v0wsin(wt) or v = v0cos(wt)
what is the formula for velocity in terms of displacement?
v = +/-w√ x0^2 - x^2
formula for Ek, Ep and Et in pendulum
Ek: 1/2mw^2(x0^2 - x^2)
Ep: 1/2mw^2x^2
Et: 1/2mw^2x0^2
formula for KE, GPE and EPE for a spring-mass system at the lowest point
KE: 0
GPE: 0
EPE: 1/2 k (e + x)^2
formule for KE, GPE and EPE for a spring-mass system at equilibrium position
KE: 1/2m^2x^2
GPE: mgx
EPE: 1/2 ke^2
formula for KE, GPE and EYE for a spring-mass system at highest point
KE: 0
GPE: 2mgx
EPE: 1/2 k (e - x)^2
explain damped oscillations
continuous dissipation of energy to the surroundings, such that total energy and hence magnitude of amplitude decreases with time
difference between light, critical and heavy damping
light: amplitude decreases exponentially but still crosses equilibrium line
critical: comes to a stop in the shortests time possible, does not cross equilibrium
heavy: takes longer than critical
explain forced oscillations
caused by continual input of energy by external applied force to compensate loss by damping to maintain magnitude of ampllitude
explain resonance
occurs when the resulting amplitude of a system becomes a maximum when the driving frequenncy of the external driving force equals to the natural frequency of the system
describe the changes to a frequency response graph as damping increases
amplitude decreases and peak shifts left
