Chapter 17 - Oscillations Flashcards
Displacement
the distance of a particle from its equilibrium position
Amplitude
Maximum displacement from the equilibrium position
Period
the time taken for one complete oscillation
Frequency
the number of oscillations per unit time
Phase difference
the fraction of an oscillation between the position of two oscillating objects
angular frequency
rate of change of angular position
Outline SHM
A type of oscillation where the acceleration of the particle is directly proportional to the displacement from the equilibrium position, and acts towards the equilibrium position.
main SHM equation
a = -ω^2x
a is acceleration
x is the displacement
ω is the angular frequency
Why is the minus sign used in the main shm equation
to show acceleration is always in the opposite direction to displacement
SHM exhibits isochronous oscillation, what does this mean?
period of oscillation is independent of amplitude
Equation for displacement of SHM oscillation starting at equilibrium position
x = Asinωt
Equation for displacement of SHM oscillation starting at amplitude position
x = Acosωt
Outline behavior of velocity and acceleration during SHM
- Acceleration max at amplitude points where displacement is max
- Velocity is max when amplitude is zero and displacement is 0 at equilibrium position
Equation for velocity in SHM
v = ±√(A^2-x^2 )
Equation for vmax of shm
vmax = ωA
Describe the energy transfers in SHM
- KE is max at equilibrium points where amplitude = 0
- PE is max at amplitude points where KE=0
Define damping
process by which the amplitude of the oscillations decreases over time. This is due to energy loss to restrictive forces such as drag or friction
outline light damping
light damping occurs naturally e.g. a pendulum oscillating in air, and the amplitude decreases exponentially.
outline heavy damping
amplitude decreases dramatically e.g. pendulum in water
outline critical damping
objects stops before one oscillation, e.g. pendulum in treacle
Outline free oscillations
when the object oscillates without any external forces being applied, it oscillates at it’s natural frequency, this is free oscillation
outline forced oscillations
when there is a periodic driving force applied to an object, which causes it to oscillate at a particular frequency
Outline resonance
when the driving force applied to an object is the same as the natural frequency of the object, resonance occurs. This is when the amplitude of oscillation rapidly increases, and if there is no damping, the amplitude will continue to increase until the system fails.
When does maximum amplitude occur regarding resonance
lowest frequency
