When does simple harmonic motion occur?
- When the force/force providing the acceleration acts towards the equilibrium position
- F ∝ -x , a ∝ -x
What is the equation for force in SHM which includes displacment?
- F = -kx
What is the equation for acceleration which includes angular velocity and extension?
- a = -ω2x
What are the two equations for displacement?
- x = Acosωt
- x = A
What are the two equations for velocity?
- v = -Aωsinωt
- v = Aω
What are the two equations for acceleration?
- a = -Aω2cosωt
- a = Aω2
What is the equation for Time period?
- T = 1/f
- T = 2π / ω
- ω = 2πf
What is the equation for time period of a pendulum and the general one?
- T = 2π (l/g)1/2
- T = 2π (m/k)1/2
State the displacement, velocity and acceleration time graphs for SHM?
Define resonance?
- When the frequency of forcing oscillation equals the natural frequency resonance occurs where max energy is transfered from driver to system causing very large oscillations
What happens when frequency of forced oscillation is not at the natural frequency?
- Minimum energy is transffered from the driver to the system so small amplitude
What are the three different types of damping?
- Underdamping
- Critical damping
- Overdamping
What happens during light and heavy damping?
- Amplitude decreases
- As energy is disipated
What happens during critical damping?
- Gets to equilibrium quickly
- Doesn’t go beyond equilibrium
What happens during overdamping?
- Amplitude drops slowly
- Doesn’t hit the equilibrium
State the graphs for overdamping, critical damping and underdamping (A against t)
What happens when a system is damped?
- Amax reduces
- Natural frequency reduces
- ETotal decreases
- Energy is disapated and transfered away from the system when work is done against opposing forces
State the graph with Energy total, Potential energy and Kinetic energy against Amplitude
What is a free oscillation?
- No driving force
What is a forced oscillation?
- Has a driving force
What happens when oscillations are forced upon a ductile material?
- Ductile material can undergo large plastic deformation before fracture
- Energy used to deform material removed from oscillating system as there is work done for plastic deformation
What happens to a resonance curve when the system is damped?
- The curve flattens and shifts to the left
What must you do first when given a resonacne question?
- Identify what is providing the forcing osicillation and what is being forced
- Forcing freq of driver = natural frequency of driven
