Topic 13 - Oscillations Flashcards
Simple Harmonic Motion
an oscillation where the acceleration of an object is directly proportional to is displacement from the equilibrium position.
conditions for simple harmonic motion
- acceleration directly proportional to is displacement from the equilibrium position.
- acceleration always towards equilibrium position
size of the force in simple harmonic motion
depends on the distance from the midpoint
time for one oscillation
is constant
as displacement from the midpoint increases…
- acceleration increases
- velocity decreases
Energy in SMH
as the object moves towards the midpoint the restoring force does work on the object so it transfers some PE to KE. When the object is moving away from the midpoint it transfers it back again.
Max KE/ Zero PE position
midpoint/equilibrium position
Max PE/ zero KE position
maximum displacement
mechanical energy
a constant value which is the sum of all the KE and PE in the system
Displacement time graph
a cosine/sin curve with amplitude A.
Velocity time graph
the derivative of the displacement time graph. With max height Aω
Acceleration time graph
The derivation of the velocity time graph. With max height Aω^2
period, t
the time for one complete oscillation
frequency time period equation
f = 1/t
frequency
the number of complete oscillations per second
amplitude
the maximum displacement from the equilibrium position
acceleration equation
a = -ω^2x
angular frequency equation
ω = 2πf
displacement time graph is sin if…
the timing starts from the centre of oscillation
displacement time graph is cos if…
the timing starts from the maximum displacement
different types of simple harmonic oscillators…
- pendulum
- mass/spring
- circular motion
When a mass on a spring is pulled/pushed either side of its equilibrium position there is a force exerted on it. This force is found by:
F = -kx
Coming F = -kx and F = ma gives
T = 2π√(m/k)
T = 2π√(m/k) condition
- only for small oscillations
- for a mass and spring system
for a pendulum the time period can be found by…
T = 2π√(L/g)
T^2 α
for a simple pendulum
Length
T doesn’t depend on…
for a simple pendulum
mass or amplitude
amplitude α
for a simple pendulum
Energy put into the system
Damping
air resistance slows the object down and energy is lost from the system by overcoming friction
What happens during damping
time period remains the same while maximum displacement reduces due to it slowing down
critical damping
damping that allows an object to move back to its equilibrium position as quickly as possible
Overdamping
doesn’t oscillate and takes a long time to move back to its original position
light damping
takes a long time for oscillations to die away
heavy damping
oscillations die away quickly
free oscillation
when you displace an object and then let it oscillate freely at its own natural
forced oscillation
when you apply an external driving force to an oscillation
natural frequency
the frequency of oscillations when there is no external force on the system
resonance
when the frequency of the external driving force is the same/ close to the natural frequency causing energy transfer to be maximised and the amplitude to grow
how is the effect of resonance reduced
damping absorbs energy therefore reduces the effect
as damping increases…
- amplitude of resonant peak decreases
- resonance peak gets broader
- resonant frequency gets lower (peak shifts to the left)
uses of resonance
- used in musical instruments
- used to tune circuits for communication
- used in digital watches
- used in medicine: magnetic resonance imaging or ultrasounds
dangers of resonance
- violently shaking buses or washing
- glass smashing
- swaying bridges
v (max) =
Aω
PE =
1/2kx^2
KE =
1/2mv^2
rubber band causing damping
work is done on the rubber band so energy dissapates to the rubber band
energy transfer in resonance
most efficient/ maximum transfer of energy
conditions for resonance
frequency of the driving force must be the same/ similar to the natural frequency of the object
a (max) =
Aω^2
explain how sound is amplified
A sounding box vibrates. The box and the thing making the sound have the same/similar natural frequencies so resonance occurs. Energy is transfer to the sounding box resulting in a larger amplitude oscillation and louder sound.
explain why amplified sound may die away faster.
The sounding box may dampen oscillations therefore a larger rate of energy transfer to the air.
what remains constant during damping
time period
when is the resultant force on a mass a minimum?
at the centre of oscillation
explain how mass dampers work
- The springs absorb energy because the springs oscillate with natural frequency of the object
- Hence there is an efficient/maximum transfer of energy
- Springs must not return energy to bridge so the energy is dissipated as quickly as possible
What equations do you show to be true when verifying SHM ?
a = ω^2x T = 2π√(m/k)
verifying SHM from a displacement time graph and an acceleration time graph
- read of the heights and calculate the displacement from the equilibrium position for each one
- plot acceleration against displacement
- should be a straight line graph through the origin with negative gradient a = -ω^2x
When will an object loose contact with an oscillating object
when the acceleration of oscillations is greater than g
how to measure the frequency of oscillations
with a stop clock measure the time for ten oscillations. calculate the time period of one oscillation. use f = 1/t to calculate the frequency.
what to include in long answer of experiment
- apparatus
- method
- accuracy precautions
derivative of cos
-sin
derivative of sin
cos
example of a forced oscillation
a car driving over a bridge
The damping force acting on an oscillating system is always
in the opposite direction to the velocity.
The restoring force on a spring system is always…
in the opposite direction to velocity
