Vibrations Flashcards
Define ‘Simple harmonic motion’
When an object moves such that its acceleration is always directed towards a fixed point and is proportional to the distance from the fixed point.
State the equation linked with SHM
a=-ω²x
a=acceleration
ω=angular velocity
x=displacment
Draw a graph for an object travelling with shm
negative gradient, straight line going through origin
a on the y axis and x on the x axis
-ω²=the gradient
As an SHM object moves it’s ____ increases a it goes further from it’s______ _____.
Acceleration increases
equilibrium position
If a=0m/s² when x=0m what a be if x is at its maximum (x=A)
a will also be at its maximum
so a max=-ω²A
A=maximum amplitude
Give the equation for the displacement of an oscillating object at a certain time
x=Acos(ωt+ ε)
ε =phase constant
for the displacement of an oscillating object at a certain time, ε is equal to what if t=0 and x=max
ε=0
for the displacement of an oscillating object at a certain time, ε is equal to what if t=0 and x=0
ε=π/2
How to calculate velocity using x=Acos(ωt+ ε)
V=-Aωsin(ωt+ε)
How to calculate maximum velocity using x=Acos(ωt+ ε)
sin(ωt+ε) max value is 1
so Vmax=-Aω x 1
Vmax=-Aω
What do both SHM equations show
The equations show that both x and v vary sinusoidally with time during SHM.
vmax when x=0m and vice versa
Describe a velocity time graph for SHM
Sine wave
V begins negative (due to x being positive)
Describe a displacement time graph for SHM
Sine wave
Displacement always begins at maximum
Describe the energy of body during SHM
A body during SHM will have a constant energy but it will transfer from potential to kinetic energy.
When Ek is max, Ep=0J and vise versa
State two examples of SHM
Two common examples of SHM are masses on a spring and a
simple pendulum.
Draw the setup for the pendulum bob experiment
Check in book for correct diagram
What is the equation for pendulum bob (acceleration)
a=-gx/l
a=pendulum bob
g=gravity
x=displacement
l=length of string
What is the equation for period in the pendulum bob experiment
T=2π√l/g
What is the set up for the mass on spring experiment
Check in book for correct diagram
What is the equation for period in the mass on spring experiment
T=2π√m/g
What is the equation for acceleration in the mass on spring experiment
a=f/m
a=-kx/m
When do free oscillations occur?
They occur when the total energy of an oscillating system stays the constant, but changes between kinetic and potential.
What is the name given to the frequency of oscillations
natural frequency
Will the frequency of oscillations stay the same, or change with time?
The frequency will not stay the same amplitude and it will decrease over time
What is the name given to the decrease in amplitude of the natural frequency over time?
Damping
What is light damping?
The period would be unchanged
What is heavy damping?
Resistive forces are significantly greater, the period is increased and barely able to complete one cycle
What is critical damping?
When the system returns to the equilibrium position in the least time possible, where the displacement is never negative
What is over damping?
It takes a very long time to return to equilibrium.
Give an examples of light damping
Vibrating strings on guitar
Give an example of heavy damping
Swinging doors that overshoot in restaurants
Give an example of critical damping
Car suspension or artillery recoil
Give an example of over damping
Earthquake protection in skyscrapers
Discuss critical damping of mtb suspension
When a mountain biker goes over a bump or does a jump, the landing isn’t so hard that it doesn’t hurt the rider’s wrist or feet. But, the suspension is not too soft either otherwise the bike would bounce upwards
Define resonance
If the frequency of the applied force is equal to the natural frequency of the system, the amplitude of the resulting oscillations is large. This is resonance.
How can resonance be useful?
Microwaves with a similar frequency to the natural frequency of a water molecule’s vibration. This increases the frequency’s amplitude and thus heating the food
How can resonance be un-useful
Frequency of the people walking on the millenial bridge was the same as the natural frequency of the bridge. Causing the bridge to oscillate
