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.
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 2. 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
What can be found from the gradiant of a graph of acceleration vs dispacement?
(2πf)2
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 readings, timing for 10 oscillations and reduce parallax errors by keeping your eye level with the start and end of an oscillation
- Plot a graph of T2 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 and reduce parallax errors by keeping your eye level with the start and end of an oscillation
- Plot a graph of T2 against l.
- Relationship is proven if the graph is a straight line through the origin.
What is damping?
The term used to describe the removal of energy from an oscillating system.
How can you tell an oscillator is being damped?
It will be losing energy so the amplitude will be decreasing
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.
Energy is lost slowly.
The amplitude of the oscillations follow an exponential decay envelope.
Describe Heavy damping
The system oscillates over a short time frame before coming to rest.
Energy is lost quickly.
The amplitude of the oscillations follow an exponential decay envelope.
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.
Doesn’t oscilate - it just stops when it first returns to the equilibrium position.
Describe over damped
The oscillating system returns to zero over an extended time frame. (No discernible oscillation)
Why does light and heavy damping take place within an exponential envelope?
At the start the oscillator has the maximum energy and maximum kinetic energy (as it passes through the mid point)
As the oscialltor is moving the quickest is has the largest value of air resistance.
The large air resistance cause energy to be lost quickly (gradient decreases quickly)
As the oscillator loses energy it slows down.
This means air resistance decreases and energy is lost as a slower rate. (gradient becomes less steep)
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 on the 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 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
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 is 90o or π/2 rad.
Above resonance the phase relationship is 180o or π rad.
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
