Oscillations Flashcards
Define frequency:
The number of oscillations per second (Hz)
Define the time period
The time taken for one complete oscillation (s)
Define amplitude:
The maximum displacement from an equilibrium position
Define Displacement
The distance from an equilibrium position.
Natural frequency
The frequency at which an object will naturally vibrate when plucked.
Resonance
When the frequency of the forced oscillator equals the natural frequency of the object, the object’s amplitude will increase to breaking point, as the energy transfer between the oscillator and the object is a maximum.
Phase difference
Difference in radians or degrees between points on the same wave or points on two waves.
Angular frequency
Is the product of 2pi x frequency
(Units of radians per second)
Dampening
Energy due to motion is lost due to resistive forces such as air or shock absorbers of a car. This causes the amplitude of motion to decrease with time.
When does an object execute simple harmonic motion?
-When the acceleration is directly proportional to the displacement.
-When the acceleration acts towards the equilibrium position
Define x=Asin(wt)
And when is this equation used?
x = displacement (m)
A= amplitude (m)
w = 2pif = angular frequency/velocity (rads^-1)
t = time (s)
Used when the oscillator starts with x=0m, at equilibrium position at t=0s
Define x=Acos(wt)
And when’s it used?
x =displacement (m)
A = amplitude (m)
w = angular frequency/ velocity (rads^-1)
t = time (s)
Used: when the oscillator starts of with x=A and at t=0s
Maximum velocity equation:
vmax = Aw
vmax= maximum velocity
A= amplitude
w = angular frequency / velocity
Equation for maximum acceleration:
amax = -w^2A
amax= maximum acceleration
w^2 = angular frequency squared
A = amplitude
What’s an isochronous oscillator?
An isochronous oscillator has a time period that is independent of the amplitude for initially small amplitude.
When do you achieve max velocity during SHM?
During equilibrium, when x=0
When do you get max acceleration during SHM?
You get maximum amplitude when x=A
How are acceleration and displacement related?
They are directly proportional to one another. However at max positive acceleration you have max negative displacement, they act in opposite directions to one another.
At x=0 and x=A describe the kinetic energy store of the SHM system:
At x=0, the mass has a maximum velocity so the KE is a maximum
At x=A, the mass has zero velocity so the KE is zero
How does the kinetic energy relate to the gravitational potential energy in a SHM system?
As KE increases, GPE decreases and vice versa.
This is for a closed system where there are no external energy transfers.
How is an oscillator dampened?
What direction do the resistive forces act in?
When is the resistive force a maximum?
An oscillator is dampened if there is a resistive force acting on it
The resistive force is in the opposite direction to the velocity of motion
The resistive force is a maximum when the velocity is a maximum which occurs at x=0m
Give examples of natural and artificial damping:
Natural: Air, Water
Artificial: Shock absorbers in buildings&cars, electromagnetic damping
Define resonance:
When the frequency at which a force is applied to an object is equal to the natural frequency of the object, the energy transfer between driver and the object is a maximum. Therefore, the amplitude will increase to a maximum and we say the object resonates.
How do you draw a dampened curve on a no damping curve?
The graph is amplitude against driving frequency.
- The maximum amplitude decreases
- The peak shifts to lower frequencies
- The range of amplitudes is always less
- The peak becomes broader
