C17 Oscillations Flashcards
What’s an oscillation?
An oscillation is a repeated motion about a fixed point (aka equilibrium position).
Angular frequency definition
Angular frequency, ω – the rate of change of angular position (given by 2𝜋f).
Whats Simple Harmonic Motion?
Simple harmonic motion, type of oscillation, where acceleration of the oscillator directly proportional to displacement from equilibrium position, and acts towards equilibrium position.
Equation used in SHM
a = - w^2x
-a, acceleration of the oscillator
-ω, angular freq
-x, displacement of the oscillator.
Negative sign used show that direction acceleration always towards equilibrium position, in opposite direction to displacement.
An oscillator in simple harmonic motion is an…
isochronous oscillation
What does isochronous oscillation mean?
the period of the oscillation is independent of the amplitude.
Fiducial marker
used as the point to start and stop timings, and is normally placed at the equilibrium position.
Equations for analysing SHM:
(When do you use each variation)?
x= Asinwt
x= Acoswt
-Used determine displacement of a simple harmonic oscillator.
-x, displacement of oscillator
-A, amplitude
-𝜔, angular frequency
-t, time
Sine version used if oscillator begins at equilibrium position.
Cosine version used if oscillator begins at amplitude position.
How is Velocity of oscillator (at a given time), determined?
finding gradient of graph at that point.
When does Max Velocity occur?
Max V occurs at equilibrium position, with oscillator being stationary at amplitude points.
When does Max Acceleration?
The max acceleration occurs at amplitude points, and is 0 when oscillator is at equilibrium position.
How can the equation v = +- w times the square root of (A^2 - x^2) be used to formulate an equation for Vmax.
-𝜔, angular frequency of oscillator
-A, amplitude
-x, current displacement
The max V occurs at equilibrium position, where x=0, so derive formula 𝑣max = 𝜔A.
What happens during SHM in terms of energy?
When does max KE and max potential energies occur?
-During SHM, energy exchanged between KE and potential forms. Max KE occurs at equilibrium point, where velocity is max.
-Max potential energy occurs at amplitude positions, where displacement at max.
-Total energy, always conserved.
Define Damping
-Process which the amplitude of oscillations decreases over time, due to energy loss to resistive forces (e.g drag or friction).
Light Damping
when damping forces are small and the period of oscillation is almost unchanged, occurs naturally (e.g. pendulum oscillating in air), amplitude decreases exponentially.
