Chapter 5 - Oscillations Flashcards
Define natural frequency?
The unforced frequency of oscillation of a freely oscillating object.
What are forced oscillations?
When each oscillation has to be forced by something else.
What are free oscillations?
Free oscillations occur when an object oscillates at its natural frequency, so it continues to oscillate after the initial disturbance.
Define period?
The time taken for one complete oscillation of an object.
Define frequency?
The number of oscillations of a particle per unit time.
Define amplitude?
The maximum displacement of a particle from its equilibrium position.
Define phase difference?
The fraction of an oscillation between the vibrations of two oscillating particles, expressed in radians.
Define phase?
Phase describes the point that an oscillating mass has reached in a complete cycle.
Define simple harmonic motion?
Motion of an oscillator where it’s acceleration is directly proportional to its displacement from its equilibrium position and is directed towards that position.
Three requirements for SHM?
1) a mass that oscillates
2) a position where the mass is in equilibrium
3) a restoring force that acts to return the mass to its equilibrium position
What is the restoring force directly proportional to in SHM?
Displacement
Define angular frequency?
The rate of change of angle expressed in radians per second (ω).
ω = ?
2πf = 2π/T
When x=0 @ t=0?
x=Asin(2πft)
When x=A @ t=0?
x=Acos(2πft)
Because a is porportional to -x, what can we deduce?
a= -x(2πf)^2
Minus since always accelerating towards equilibrium position.
Vmax = ?
Vmax = (2πf)A
When do the maximum PE and KE points happen?
PE is maximum at the amplitude.
KE is maximum at x=0.
Energy against time graph for SHM?
PE starts at max because system is starting at A. This means KE is at zero.
When the system is released KE increases and PE decreases, causing a two sine waves in antiphase.
ENERGY REMAINS CONSTANT.
Energy against amplitude graph?
Symmetrical about y axis.
As you approach A, KE falls and PE rises. At x=0, PE is minimum, KE is maximum.
Define damped, and 2 points about it?
Describes an oscillatory motion where the amplitude decreases with time due to energy losses.
1) causes displacement to decreases exponentially
2) used in car suspension - springs have shock absorber so the car doesn’t continuously bounce.
Define resonance?
The forced motion of an oscillator characterised by max amplitude when the forcing frequency matches the oscillator’s natural frequency.
For resonance to occur, the system has to absorb maximum energy. When will this occur?
When the source frequency = natural frequency of the system
Three points for a system in resonance?
1) natural frequency is equal to driver frequency
2) amplitude is maximum
3) it absorbs greatest possible energy from the driver
Describe a amplitude against driver frequency graph?
The amplitude of the system reaches a maximum at the peak of the line when natural frequency = driver frequency.
Explain what happens to the graph of amplitude against driver frequency, with damping?
With damping, the peak (A) is lower, and moves to a slightly lower resonance frequency(left). Also, the peak becomes broader.
Where is resonance used?
In instruments, MRI and microwaves. In microwaves, it is used to vibrate the water molecules at their natural frequency,
Define oscillation?
A repetitive back and forth motion about the equilibrium position.
