SHM revision Flashcards
To revise SHM
What is the period of oscillation?
The time for one complete cycle of oscillation.
If a trolley is at equilibrium attached to two springs, when pushed in one direction, what will the trolley do and why?
It will accelerate toward the equilibrium point.
The extended spring provides a restoring force.
What is natural frequency?
The frequency of free oscillations of an oscillating system.
What are forced vibrations?
Making an object oscillate at a frequency that is not it’s natural frequency
When does resonance occur?
When the driving force or oscillation matches the natural frequency of the system.
What is the outcome of resonance?
An increase in amplitude of the system’s oscillation.
What is damping?
The term used to describe the removal of energy from an oscillating system.
What are the four levels of damping?
Light
Heavy
Critical
over damped
Describe light damping of a system
The system oscillates over a long time frame before coming to rest.
The amplitude of the oscillations follow an exponential decay envelope.
Describe over damped
The oscillating system returns to zero over an extended time frame.
(No discernible oscillation)
Describe critical damping
The oscillating system returns to the zero position of the oscillation after one quarter of a time period.
Does not affect frequency.
Define a free oscillator
Oscillations where there is no periodic force acting on the system
Define a forced oscillator
A system is forced to oscillate by an external periodic force
For an object undergoing SHM where does it have the greatest velocity?
At the equilibrium position
For an object undergoing SHM where does it have zero velocity?
At the amplitudes
For an object undergoing SHM where does it have the greatest acceleration?
At the amplitudes
For an object undergoing SHM where does it have the least acceleration?
At the equilibrium point
State the two conditions required for SHM
- Acceleration always directed towards the equilibrium position
- The acceleration is proportional to the displacement of the object from the equilibrium position
What is the relationship between displacement and frequency for a shm oscillator?
They are independent.
As displacement increases the accelerations increases. this increases the average velocity which cancels out the additional distance the oscillator needs to travel
What is the relationship between mass and frequency for a shm oscillator?
As mass increases the accelerations decreases (F=ma)
the lower acceleration causes a lower average velocity. This means time period will increase and from f = 1/T then frequency will decrease
What is the relationship between spring constant and frequency for a shm oscillator?
As spring constant increases the resting force increases (F=ke). This causes a larger acceleration (F = ma) which means the average velocity will be greater. The will reduced the time period and increase the frequency (f = 1/T)
Describe the displacement against time graph for an oscillator starting at the right hand side amplitude
Sin (x)
Describe the velocity against time graph for an oscillator starting at the right hand side amplitude
cos (x)
Describe the acceleration against time graph for an oscillator starting at the right hand side amplitude
-sin (X)
What function should your calculator be in when using the displacement equation
Radians
Describe the acceleration against displacement graph for a SHM oscillator
A straight line through the origin with a negative gradient
Describe the velocity against displacement graph for a SHM oscillator
A circle with the origin as the mid point
Describe the kinetic energy against displacement graph for a SHM oscillator
a n shape
Describe the potential energy against displacement graph for a SHM oscillator
a u shape
For a mass spring system plan a practical to prove the relationship between time period and mass
Vary the mass 8 times.
Measure the time period
Keep spring constant a control variable
make the experiment more accurate by repeat reading, timing for 10 oscillations
Reduce parallax errors by keeping your eye level with the start and end of an oscillation
Plot a graph of Tsquared against m.
Relationship is proven if the graph is a straight line through the origin.
For a pendulum plan a practical to prove the relationship between time period and length
Vary the length 8 times.
Measure the time period
Keep mass of the pendulum bob a control variable
make the experiment more accurate by repeat reading, timing for 10 oscillations
Reduce parallax errors by keeping your eye level with the start and end of an oscillation
Plot a graph of Tsquared against l.
Relationship is proven if the graph is a straight line through the origin.
How can you tell an oscillator is being damped?
It will be losing energy so the amplitude will be decreasing
Describe Heavy damping
The system oscillates over a short time frame before coming to rest.
The amplitude of the oscillations follow an exponential decay envelope.
What is the effect of increasing damping on an oscillator that is resonating
the amplitude of vibrations at any frequency decreases
resonance occurs at a lower frequency
The peak becomes flatter and broader
State some examples where resonance is useful
Microwaves heating water molecules
An antenna receiving a radio signal
Musical instruments
State some examples where resonance is a nuisance
wind causing bridges to oscillate
Buildings during an earthquake
Sand is placed on a surface oscillating up and down, explain why above a certain frequency, the sand loses contact with the surface (3)
When the vibrating surface accelerates down with an acceleration less than g, the sand stays in contact
Above a particular frequency, the acceleration is greater than g
There is no contact force on the sand
State the phase relationship between the driving force and the object that is oscillating
Below resonance they are in phase with each other.
At resonance the phase relationship is90o or π/2 rad.
Above resonance the phase relationship is 180o or π rad.
