13 Oscillations Flashcards
Amplitude
Max displacement of a particle from the equilibrium
Frequency
Number of oscillations per second
Time period
Time taken to complete one oscillation
Equations for time period
T = 1/f
T = 2pi/angular speed
Simple harmonic motion
The oscillatory motion about an equilibrium position such that the acceleration is proportional to the displacement and always directed towards the equilibrium position
What equation is simple harmonic motion defined by
a = -w^2 x X
How could a displacement time graph be found using an experiment
The transmitter of a displacement sensor could be attached to a mass on a spring which oscillates
What is the equation for the SHM displacement graph
X = A x cos(wt)
Equation for SHM velocity graph
V =-A x w x sin(wt)
Equation for SHM acceleration graph
a = -A x w^2 x cos(wt)
What is the maximum displacing equal to?
Amplitude
What is the maximum velocity equal to?
A x w
What is the maximum acceleration equal to?
A x w^2
Equation for mass on spring
F = -kx
F= force k= stiffness/ spring constant x= displacement
Mechanical oscillator equation linking time period, mass and spring constant
T =2pi x route(m/k)
Equation for pendulum linking time period, length and gravity
T= 2pi x route(l/g)
For what angles does a pendulum display simple harmonic motion
Less than 10° to the vertical
What is true of the time period of a heavy mass on a weak spring?
It’s large
What are the two main forms of energy in simple harmonic oscillators?
KE and PE
Equation for kinetic energy (learn)
KE = 1/2mv^2
KE = 1/2m x A^2 x w^2 x sin^2(wt)
Equation for potential energy (learn)
PE= 1/2kx^2
PE= 1/2m x A^2 x w^2 x cos^2(wt)
Equation for total energy (learn)
E total= PE + KE
E total= 1/2m x A^2 x w^2
Free oscillations
When no energy is lost from an oscillator so the motion would continue would continue forever
Damped oscillation
When energy is transferred out of the system
Forced oscillations
When a system is made to vibrate at the frequency of an external driving force
How does the amplitude of an oscillation change with light damping?
The amplitude decreases exponentially over time
Example of a system with light damping
Pendulum oscillating in air
How does the amplitude of an oscillation change with heavy damping?
The amplitude returns to the equilibrium slowly
Example of system with heavy damping
A spring in thick oil
How does the amplitude of an oscillation change with critical damping?
the time taken for displacement to become zero is a minimum
Example of critical damping
Shock absorbers of a car
What happens if oscillations are forced on ductile materials
Energy will be absorbed due to plastic deformation and motion will be damped
Resonance
Takes place when the applied frequency equals the natural frequency of an oscillator
In theory what should happen to amplitude of a system in resonance?
It should be infinite as energy is continually being put into the system but in practise it is reduced by damping
How does damping affect the resonant frequency
If damping is increased the resonance occurs at a lower frequency
How does damping affect the amplitude
It reduces the amplitude
Examples of resonance occurring?
- opera singer smashing glass
- microwaves
- radios
Which of the following can’t apply to the oscillations of a system undergoing resonance?
A) damped
B) driven
C) forced
D) free
D) free
When a mass on a spring is in the equilibrium position, what is the elastic potential?
At a maximum
During an earthquake, steel framed buildings absorb energy because steel is
A) ductile
B) elastic
C) stiff
D) strong
A) ductile
How do spring dampers reduce the amplitude of an oscillating bridge?
- they absorb energy
- the springs oscillate with the natural frequency
- hence there is max transfer of energy
- spring must not return energy back to bridge
Which of the following is not an example of SHM?
A) a car bouncing on its suspension system
B) a child bouncing on a trampoline
C) a person bouncing on a bungee cord
D) a swinging pendulum in a grandfather clock
B) a child jumping on a trampoline
When will the motion of a mass bouncing on the end of a vertical spring be simple harmonic?
A) if the string can store energy
B) if it has elasticity
C) is hung vertically
D) obeys hookes law
D) obeys hookes law
Damping is used to prevent a bridge from oscillating, it will
A) increase the stiffness of the bridge
B) increase the natural frequency of the bridge
C) dissipated energy from the bridge
D) decrease the forcing frequency on the bridge
C) dissipate energy from the bridge
The damping force acting on an oscillating system is always
A) in the opposite direction to acceleration
B) in the opposite direction to velocity
C) in the same direction as acceleration
D) in the same direction as velocity
B) in the opposite direction to velocity
When a mass is oscillating on a vertical spring which obeys hookes law what happens to the time period over time?
It stays constant because the spring obeys hookes law
