Chapter 5: Oscillations Flashcards
Define free oscillation
An object oscillates at its natural frequency
Give 3 examples of free oscillations
- Vibrations of a guitar string when you pluck it 2. Vibrations of a tuning fork when you strike it 3. Oscillation of a child in a swing
Define oscillation
An object moves back and forth repeatedly on either side of its equilibrium position
Define displacement
The distance an object has moved from its equilibrium position
Define amplitude
Maximum displacement of an object from its equilibrium position
Define period
The time for one complete oscillation (one side to the other and back again)
Define frequency
Number of oscillations per unit time
Define angular frequency
The rate of change of angle in radians per second = 2pi x frequency
Define phase difference
The fraction of an oscillation between the vibrations of two oscillating systems expressed in radians or degrees
3 requirements for SHM
- Mass that oscillates 2. Equilibrium position 3. Restoring force that returns the mass to its equilibrium position
Explain why period of an object with SHM is independent of amplitude
- If you plot a graph of a=-(2pif)^2x it is a straight line with -ve gradient of (2pif)^2 through the origin 2. The gradient of the graph is independent of the amplitude 3. Therefore frequency also independent so the oscillator keeps steady time
Describe and draw the graph for the change of displacement in SHM
Sine curve starting at: a) (0,0) if beginning at equilibrium position b) (0,A) if starting at amplitude Max. displacement = amplitude
Describe and draw the graph for the change of velocity in SHM
-Velocity = rate of change of displacement -So graph = grad. of x/t graph -Phase diff. of 90 degrees w. x/t graph
Describe and draw the graph for the change of acceleration in SHM
-Acceleration is rate of change of velocity -So graph = gradient of v/t graph -a=-kx so it is also a reflection of x/t graph in x axis
Describe and explain the interchange between k.e. and p.e. in SHM
-Total energy is constant for an undamped system -k.e. max. at equilibrium position -p.e. max. at amplitude -Energy changes between k.e. and p.e.
Draw an energy/time graph for SHM
-Sine graph w. k.e. and p.e. -1 oscillation = 2 full waves on graph -Energy cannot be -ve
Draw an energy/displacement graph
x-axis has -A to +A -Energy cannot be -ve
Describe effects of damping on an oscillating system
- Oscillations lose energy due to friction 2. Amplitude of oscillations decreases exponentially 3. Frequency does not change (SHM) -@ start movement large so high air resistance and energy lost quickly -moving slower so less air resistance so energy lost less quickly
Give an example of a forced oscillation
- Sitting on bus engines vibrations cause you to oscillate
Describe and explain resonance using a graph
Amplitude/driving frequency graph 1. In resonance energy is transferred to the system most efficiently so absorbs greatest poss. energy 2. Natural f = f of driver 3. Amplitude is maximum
Give 3 examples of useful resonance
- Microwaves: f of microwaves (driver) = natural f of water mols in food -> heats food as water absorbs energy 2. MRI: f of radio waves (driver) = natural f of hydrogen nuclei 3. Radio/TV aerial: tuner adjusted so natural f = f of chosen station (driver) so circuit produces large current for this f only
Give 3 examples where resonance is harmful and solutions
- Car springs: vibrate when going over a bump -> damped by shock absorbers 2. Buildings: during earthquake forced to oscillate by vibrations of the earth (driver) -> shock absorbing foundations 3. Suspension bridges: wind causes resonance and damages bridge
Give 3 examples of SHM
- Vibrating strings of a musical instrument 2. Alternating current electrons vibrate with SHM 3. Atoms in a molecule vibrate with SHM
Describe acceleration in SHM
- Directly proportional (but opp. direction) to displacement from equilibrium position 2. Always directed towards equilibrium position
In SHM what is the relationship between max v and A
Directly proportional: 1. SHM has T independent of A 2. If A increases, the object will have to travel a greater distance in the same amount of time so will have to move faster
What’s the relationship between max v and frequency in SHM
Directly proportional 1. If the frequency increases T goes down 2. Therefore a given distance must be covered in a shorter time so speed increases
What happens to energy when oscillations are damped
- Energy is removed from the system as heat by friction 2. A and max v decrease
