Unit 3.2 - Vibrations Flashcards
2 categories of all motions
Periodic motion
Non-periodic motion
Periodic motion
An object repeats the same pattern of motion over certain periods of time (e.g - butterfly wings and machines)
What’s the problem with the pattern of periodic motion
Often complex and difficult to analyse
What do we use to help us analyse periodic motion? Why?
Use motion in a circle, as it’s also periodic and is easier to understand
Oscillator
An object moving backwards and forwards in a periodic motion
Oscillation
The motion of the oscillator
Period
The time taken for one oscillation (s)
Frequency
The number of oscillations in a fixed amount of time (per second)
Amplitude (when describing simple harmonic motion)
The largest displacement form the undisturbed position (m)
Phase (when describing simple harmonic motion)
The relationship cycle between 2 systems oscillating or between 2 points in a single oscillation
How could you describe 1 complete oscillation?
Motion from one point, passing through all the other points, passing through all the other points on the line and returning to the original position
What is independent of the amplitude of the oscillator during simple harmonic motion?
Period
Equation for acceleration towards the centre of a circle and how it’s adapted for simple harmonic motion
a = ω^2r
In simple harmonic motion, the acceleration has an inverse relationship with the distance from the midpoint, so the RHS becomes negative, and r is replaced with x (displacement)
a = -ω^2x
What does acceleration have an inverse relationship with in simple harmonic motio?
Distance from the midpoint
What 3 things can be deduced from the equation a = -ω^2x?
The acceleration is proportional to the displacement
The direction of the acceleration is opposite to the direction of displacement
The motion’s acceleration is only dependent on the period and the displacement
What is simple harmonic motion’s acceleration dependent on?
The period and the displacement (not the amplitude)
Why is simple harmonic motion called this?
Sinusoidal motion and a pretty straightforward equation
Simple harmonic motion definition
Simple harmonic motion occurs when an object moves such that its acceleration is always directed towards a fixed point (equilibrium position) and proportional to its distance from the fixed point
In which direction is the force causing simple harmonic motion?
In the same direction as the acceleration
Relationship between the force and displacement from the centre point in simple harmonic motion
The force is directly proportional to the displacement from the centre point and is always directed towards it
How do we know if an x vs t graph uses a cos function?
It starts at a maximum (x=A when t=0), then at t = T/2 the displacement is A again. The displacement is at zero exactly halfway between t=0 and t=T/2, then is at A again at t=T
How does the graph of displacement against time repeat its motion for simple harmonic motion?
With a period of T
How do we model the displacement (x) sinusoidally from a cos graph of displacement against time?
We need to relate time t to an angle
The period of a sine graph = 2pi radian
So, to construct the model, we multiply t by 2pi/T radian s-1
So, when t=T —> 2pi/T = 2pi radian
How come x=A when t=0, T and 2T on the displacement against time graph?
Using x ∝ cos (2pi/T x t)
The equation gives +1, which is the maximum value of cos