5.3 Oscillations Flashcards
Displacement
The distance an object is from it’s rest position
Amplitude
Maximum displacement
Frequency
The number of oscillations per unit time at any point
Angular Frequency and its symbol
(ω) The product 2pi*f
Phase Difference and its symbol
(Φ) The fraction of a complete cycle between two points, expressed in radians
Simple Harmonic Motion
An oscillating body where the acceleration of the body is directly proportional to its distance from a fixed point (its equilibrium position) and this acceleration is always directed to the fixed point
SHM defining equation
a=-(ω^2)x
Solutions to the equation a=-ω^2x
x = Acosωt, x = Asinωt
Equation for velocity
v = +-ω*root(A^2-x^2)
Maximum acceleration
(Sub in A for x) max a = Aω^2
Maximum velocity
(Sub in A for x) max v = Aω
Maximum displacement
A
Investigation for SMH
Set up a mass on a spring hanging from a clamp stand. Place a position sensor beneath it. Pull down the spring and let it oscillate with its displacement being recorded. When plotted against time it should resemble a sine wave with decreasing amplitude.
What effect does increasing the mass on a spring have on SHM time period
Longer time period
What effect does the stiffness of the spring have on SHM time period
High stiffness = short time period
What effect does increasing the initial displacement have on SHM time period(with a spring)
No effect on time period
What effect does increasing the initial angle of a pendulum have on SHM time period
No effect on time period
What effect does increasing the mass of a pendulum have on SHM time period
No effect on time period
What effect does increasing the length of the string of a pendulum have on SHM time period
Increases time period
How is angular frequency related to angular velocity
Angular frequency is the magnitude of the angular velocity
If x = Asinωt what is velocity and acceleration
v = ωAcosωt a =-ω^2Asinωt (just differentiate)
How is mechanical energy affected during SHM
Not affected
How is kinetic energy affected during SHM
Maximum at equilibrium, minimum at highest displacement
How is potential energy affected during SHM
Minimum at equilibrium, maximum at highest displacement
Draw the graph of displacement against kinetic and potential energies
PE is a U
KE in ^
Natural frequency
The frequency a system will oscillate at when undergoing free oscillation
Forced Oscillation
A periodic driving force is applied to the system causing it to oscillate at the same frequency as the driving force
Driving frequency
The frequency with which the driving force is applied to the oscillating object
Resonance
Occurs when the driving frequency is equal to the natural frequency of the body being forced to oscillate. The body will oscillate at it’s natural frequency and its maximum amplitude
Damping
Damping forces reduce the amplitude of an oscillation with time by removing energy from the system
Critical damping
Reduces the amplitude in the shortest possible time
Overdamping
The system does not oscillate but it takes longer to return to its equilibrium than with critical damping
What does a graph of frequency against amplitude look like
sharp peak around natural frequency
How does damping affect resonance
Reduces the maximum amplitude of resonance
Examples of resonance (4)
- Organ - Swing - Glass smashing - Radio
