M5C3 Flashcards
Define simple harmonic motion (S.H.M)
A body will oscillate with simple harmonic motion if it’s acceleration is directly proportional to its displacement from a fixed point and always directed towards that fixed point
How do you calculate phase difference?
ɸ = 2πΔt/T ɸ = d/λ 2π T = period (s) f = frequency (Hz) ɸ = phase difference (rad) d = distance between two points
What are the equations for angular velocity?
ω = 2πf ω = 2π/T T = period (s) f = frequency (Hz) ω = angular frequency (rad s-1)
Define amplitude
The distance in meters from the center of rotation
Define phase difference
The fraction of a complete cycle or oscillation between two oscillating points
What is the equation for displacement when starting at maximum displacement and the minimum displacement?
x = Acosωt (maximum) x = Asinωt (minimum) x = displacement (m) A = maximum displacement (m) ω = angular frequency (rad s-1) t = time (s)
What is the equation for velocity when starting at maximum displacement and the minimum velocity?
x = -ωAcosωt (maximum) x = -ωAsinωt (minimum) x = velocity (m s^-1) A = maximum displacement (m) ω = angular frequency (rad s-1) t = time (s)
Define isochronous
Constant and independent to the amplitude of any oscillation (occurring at the same time)
Define isochronous
Constant and independent to the amplitude of any oscillation (occurring at the same time)
What is the equation for frequency?
f = 1/T f = frequency (Hz or s^-1) T = time period (s)
When a pendulum is moving with simple harmonic motion what is it’s total energy equal to?
Total energy = GPE + KE
As GPE falls KE rises and vice versa
When a spring is moving with simple harmonic motion what is it’s total energy equal to?
Total energy = GPE + KE + EPE
Define damping
Damping forces reduce the amplitude of an oscillation with time, due to the energy being removed from the oscillatory system
When is damping considered natural damping
When the damping forces are caused by natural forces (e.g. friction and air resistance)
What is artificial damping?
When damping forces are caused by artificial forces
What’s natural damping?
Damping caused by natural forces (frictional forces) for example air resistance
When is damping considered artificial?
When damping forces are caused by external or manmade factors an example of this is a shock absorber in a car
Explain light damping
When the amplitude of the oscillation decays slowly with time (exponential decaying to zero) due to the energy removed from the oscillatory system
Explain heavy damping
When the amplitude of the oscillation decays and the time period of the oscillation slightly increases each cycle
state what is meant by very heavy damping
No oscillation occurs and the body slowly moves back equilibrium
What is resonance?
When the driving frequency is equal to the natural frequency of the system that’s oscillating. Results in the body oscillating at its natural frequency with maximum amplitude.
Define free oscillation
Occurs when there is no external periodic force present. The system is oscillating at its natural frequency
Define natural frequency
The frequency a body will oscillate at when it’s undergoing free oscillation
What is forced oscillation?
When an external force, driving force, is applied to a body to keep the body oscillating. The system oscillates at the frequency of the driving force
What is meant by driving frequency?
The frequency at which the driving force oscillates.
What happens in a forced oscillation?
With a system that is subject to forced oscillations there will always be at least 2 objects that are oscillating;
1st object – The object (driver object) causing the vibration. This objects frequency is called the ‘driving frequency’.
2nd object – This object (slave object) is being made to oscillate due to object 1’s oscillatory motion. Object 2 will have a ‘natural oscillatory frequency’.
