Further Mechanics Flashcards
Simple Harmonic oscillation definition
An oscillation in which the acceleration of the object is directly proportional to its displacement from it’s equilibrium position, and is directed towards the equilibrium
SHM velocity equation
V= ω sqrt(A^2-X^2)
SHM velocity equation
V= ω sqrt(A^2-X^2)
Maximum velocity equation
Vmax= ωA
Maximum velocity equation
Vmax= ωA
Displacement equation
x=Acos(ωt)
Acceleration equation
A=-ω^2 x
Amax= ω^2A
Angular velocity (ω) equation
ω=2πf=2π/T
ω=V/r
ω= θ/t
What is the total energy equal to at the equilibrium
Maximum kinetic energy
What is the total energy equal to at the amplitude
Maximum potential energy
Centripetal acceleration equation
a= ω^2 r
a=v^2 / r
Centripetal force equation
F=mω^2r
F=mv^2/r
What happens when something moves in a circular path and the centripetal force is removed?
The object will fly off at a tangent
Time period for a simple pendulum
Time period for a mass-spring system
T=2π sqrt(l/g)
T=2π sqrt(m/k)
What can the time period equation for simple pendulums be used
Only for small oscillations
Angles under 10 degrees
What is the centripetal force of an object equal to at the TOP of a vertical circle
F=T+W
What is the centripetal force of an object equal to at the BOTTOM of a vertical circle
F=T-W
Free vibration
-Involves no transfer of energy to or from surroundings
-Objects oscillate at resonant(natural) frequency
Forced vibration
-External driving force that’s periodic
-Applied at driving frequency
Forced vibration
-External driving force that’s periodic
-Applied at driving frequency
What is resonance?
-When the driving frequency = natural frequency
-Maximum energy transfer
-Rapid/dangerous increase in amplitude
When the driving frequency is less than natural frequency, what is the amplitude and phase difference(between driver and oscillator)
Amplitude= same as driver
Phase difference= 0 (in phase)
When the driving frequency is the same as the natural frequency, what is the amplitude and phase difference(between driver and oscillator)
Amplitude= Very large
Phase difference= π/2
When the driving frequency is greater than natural frequency, what is the amplitude and phase difference(between driver and oscillator)
Amplitude= small
Phase difference= π
What is damping?
Oscillator experiences resistive force that removes energy from it
Always acts in the opposite direction to motion
With what types of damping does the time period not change?
Light and heavy
How does damping affect amplitude?
It can reduce it but not stop it completely
Why is acceleration proportional to negative displacement?
Because it is always directed towards the equilibrium
What effect does damping have on resonance?
No effect
Damping just reduces amplitude
What are 2 measures to reduce size of oscillations
Use shock absorbers
Use a material with a high natural frequency
Displacement against time graph
Cos graph
Velocity against time graph
Negative sin graph
Acceleration against time graph
Negative cos graph
Velocity against amplitude graph
Circle
Acceleration against amplitude graph
Straight line negative through origin
Phase difference when resonance happens
Pi/ 2
