Chapter 17: Oscillations Flashcards
Simple Harmonic Motion
An oscillation in which the acceleration of an object is directly proportional to its displacement from the midpoint, and is directed towards the midpoint
Restoring Force
pushing or pulling object back towards equilibrium position, size depends on displacement and can cause acceleration
acceleration of SHM equation
a = -ω^2 x
Gradient of velocity-time graph
Displacement
distance from equilibrium position
Varies as a cosine or sine graph with max value A
Amplitude
maximum displacement
period
time taken for one oscillation
frequency
number of oscillations per second
Conditions for SHM
- acceleration must be directly proportional to displacement and in the opposite direction
- must always act towards the equilibrium
Two examples of systems that undergo SHM
- mass-spring system
- pendulum
True or false: velocity is maximum when displacement is maximum
False.
Velocity is at minimum when displacement is maximum
Velocity is max at equilibrium position
What is damping?
Process by which the amplitude of the oscillator decreases over time. This is due to energy loss to resistive forces such as drag and friction
Light damping
occurs naturally
amplitude decreases exponentially
Sharp resonance peak
Heavy damping
amplitude decreases dramatically
Critical damping
Object stopped in s short time without overshooting the pendulum
Difference between free and forced oscillations
Free - oscillations without external forces, at natural frequency
Forced - periodic driving force is applied, particular frequency
Resonance
Driving frequency of the external force is applied to an object is same as the natural frequency of object
no damping
amplitude of oscillation rapidly increase
Energy changes during SHM
exchanges between potential energy and kinetic energy
mechanical energy
sum of kinetic and potential energy
Phase Difference
how much one wave lags behind another
measured in Radians
Is there a relationship between frequency, period and amplitude?
No.
Frequency and period and independent of amplitude
How do potential and kinetic energy vary through SHM?
- Towards equilibrium: P transferred to K
- Away from equilibrium: K transferred to P
- Equilibrium: K max and P=0
- Max displacement: K=0 and P max
SHM Experiment
1) Lift mass slightly and release it. Mass-spring system will start oscillating with SHM
2) Experiment must be repeatable, place ruler behind the spring to measure how far to raise the mass
3) As mass oscillate, position sensor will measure displacement over time
4) Let experiment run until you have good amount of data
Computer will generate displacement-time graph and from graph you can obtain A and T
What happens when damping increases?
- Amplitude at any frequency decreases
- Maximum amplitude occurs at a lower frequency than f0
- The peak on the graph becomes flatter and broader
Forced Vibration
periodic force, alternating force applied to a mechanical system
