Oscillations
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Define displacement.
Distance from the equilibrium position
Define amplitude
Maximum displacement from the equilibrium position
Define period
Time taken to complete one oscillation
Define frequency
The number of complete oscillations per unit second.
What is angular frequency?
The rate of change of the angular position
Two equations for angular frequency?
2π / T 2 π f
Define simple harmonic motion.
A type of motion where the acceleration is directly proportional to the displacement and acts towards the equilibrium position.
Defining equation for SHM?
a = - ω^2 x
What does an acceleration against displacement graph look like for an object oscillating in SHM?
Straight-line graph. Check Notion.
What is oscillating motion?
• Object is in equilibrium position. • Force applied. • Object displaced then oscillates.
What are two features of SHM that can be inferred from the equation?
• acceleration ∝ displacement - minus sign means that acceleration and displacement act in opposite directions
Is angular frequency constant in SHM? What does this mean?
Yes. f and T are constant
Suggest two ways you could investigate the time period and frequency of objects moving with SHM.
• Pendulum with mass attached. - Spring.
Suggest two reasons why a fiducial marker should be placed at POE
• Object will always pass POE (unlike maximum displacement position) • Reduces uncertainty in timing measurements
How can you investigate the time period of an object moving in SMH?
Record time taken for several oscillations -> less uncertainty due to human error
What is an isochronous oscillator?
An oscillator that has the same T period regardless of the amplitude.
Why is time period independent of amplitude in SHM?
As amplitude increases, speed increases so time period is constant.
Equations to find the displacement of an object oscillating in SMH?
x = A cos ω t (Starts at amplitude) x = A sin ω t (Starts at POE)
What happens when the ω of an oscillator increases with no change to the amplitude?
Time period changes -> Velocity changes
What happens to velocity when amplitude increases?
• Isochronic oscillator = same time period - Travel greater distance in same time period -> velocity increases
Equation to find velocity of a simple harmonic oscillator?
V = ± ω √ A^2 - x^2
Equation to find V max of a simple harmonic oscillator
V max = ω A
What does an energy against displacement graph look like for an object oscillating in SHM?
Two parabolas. Check Notion
How do you work out the Ek of a mass-spring system?
Ek = Et - Ep Ek = 1/2 k (A^2 - x^2)