Oscillations Flashcards
What is an oscillation?
The repetitive variation with time of the displacement of an object about the equilibrium position
What is displacement (x)?
The distance of a point on the wave from its equilibrium position
What is amplitude (x0)?
The maximum value of the displacement on either side of the equilibrium position
What is the period (T)?
The time interval for one complete oscillation to occur
What is frequency (F)?
The number of oscillations per second
What is phase difference?
A measure of how much a point or a wave is in front or behind another
What is angular frequency (ω)?
The rate of angular displacement with respect to time
What are the main angular frequency equations?
ω = 2pi / T
ω = 2pi f
T = time period
f = frequency
What is simple harmonic motion?
An oscillation where the acceleration of a body is proportional to its displacement but acts in the opposite direction
a ∝ - x
What are the 3 conditions for simple harmonic motion?
- The acceleration is proportional to the displacement
- The acceleration is in the opposite direction to the displacement
- The acceleration is always directed towards the equilibrium position
What is the simple harmonic motion equation?
a = -ω^2 x
a = acceleration
ω = angular frequency ( rad s^-1)
x = displacement
What does an isochronous oscillation mean?
The period of the oscillation is independent of the amplitude
What type of oscillations occur when an oscillator is in simple harmonic motion?
Isochronous oscillations
How can you determine the period and frequency on SHM oscillations - using hanging masses?
How can you determine the period and frequency on SHM oscillations - using a pendulum?
What equation is used to find the position of an object in SHM when the object began oscillating at the equilibrium position?
x = A sin ωt
What equation is used to find the position of an object in SHM when the object began oscillating at the amplitude position?
x = A cos ωt
When does the maximum velocity of an oscillator occur?
At the equilibrium position
What is the velocity, angular frequency, amplitude and displacement equation?
where x0 = amplitude
What are the maximum velocity equations?
v = v0 cos ω
v0 = ωA
where v0 is maximum velocity
What is the SHM displacement-time graph?
What is the SHM velocity-time graph?
What is the SHM acceleration-time graph?
What is energy constantly changing between for simple harmonic motion?
Between kinetic and potential energies
What is the potential energy type for a pendulum?
Gravitational potential energy
What is the potential energy type for a horizontal mass on a spring?
Elastic potential energy
When is the KE at a maximum in SHM?
When the displacement equals 0 - equilibrium position
Why is KE maximum at the equilibrium position?
Because velocity is maximum at equilibrium and KE = 1/2 mv^2
When is KE zero during SHM?
At amplitude position
When is potential energy at a maximum during SHM?
When the oscillator is at amplitude position
What does the total energy of a simple harmonic system do?
Stays constant during oscillations - its constantly exchanges between kinetic and potential energies, when one increases the other decreases and vice versa
What is the energy of a SHM oscillator equation?
E = 1/2 m ω^2 A^2
E = total energy of a simple harmonic system
m = mass of oscillator (kg)
ω = angular frequency (rad/s)
A = amplitude (m)
What does the graph for energy against displacement look like for a simple harmonic system?
What is a free oscillation?
An oscillation where there are only internal forces (and no external forces) acting, and there is no energy input
What is a free vibration?
A vibration that always oscillates at its resonant frequency
What is a forced oscillation?
Oscillations that are acted on by a periodic external force where energy is given in order to sustain oscillations
Why do all systems eventually stop oscillating?
Because of resistive forces - such as friction or air resistance - that act in the opposite direction to the motion of oscillations
What is damping?
The reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system
How long does damping have an effect for?
Until the oscillator comes to a stop
What does not change when an oscillating system becomes damped?
The frequency - it remains the same with the decreasing amplitude
What is light damping?
Damping that causes the amplitude to decrease gradually - it decays exponentially with time
What is critical damping?
Damping that when displaced the oscillator will return to rest at its equilibrium position in the shortest possible time without oscillating
What is heavy damping?
Damping that when displaced, the oscillator will take a long time to return to its equilibrium position with without oscillating
What types of damping occur with no more oscillations happening?
Critical & heavy
What is a driving frequency?
The frequency of forced oscillations
What is natural frequency?
The frequency of an oscillation when the system is allowed to oscillate freely
What is resonance?
When the frequency of the applied force to an oscillating system is equal to its natural frequency, the amplitude of the resulting oscillations increases significantly
What does resonance look like graphically?
What reduces the amplitude of resonance vibrations?
Damping
What does different levels of damping when resonance occurs look like graphically?
What are the purposes of resonance?
- In an organ pipe - the air molecules resonate to an increase in amplitude of sound
- Radio receivers - the resonance of the radio waves allows the signal to be amplified by the receiver to listen
- Microwave oven
