Module 5 Simple Harmonic Motion Flashcards
Where is velocity at a maximum?
at the mean position when x = 0
Where is velocity zero?
at the amplitude when x = +A or -A
Explain why at the amplitude, velocity is zero?
mass is changing direction, velocity zero for an instant
What is the definition for amplitude considering SHM?
the maximum displacement from the equilibrium/mean position
Explain how a graph of displacement against time and acceleration against time can be used to show that they are directly proportional but in opposite directions?
Comparison of the two graphs shows a phase difference of 180°
Define simple harmonic oscillation?
a type of oscillation where acceleration is directly proportional to displacement but in the opposite direction
What is the symbol for angular displacement?
omega ω
What are the units for ω?
the units for angular frequency ω are rad*s^-1
When is the formula x=Asin(ωt) used over x=Acos(ωt) used?
When at t=0 the displacement is zero, use sin
Explain how when using x=Acos(ωt), if t=T where T is the time period, will the displacement be the amplitude
Calculation in radians
ωt=ωT and ω=2π/T
So ωT=2π
cos(2π) = 1
1xA = A
How you find the maximum velocity of an object in SMH?
Vmax=±ωA (originally (A^2-x^2) cancels out to A^2 as displacement x is zero at max velocity)
Describe how to plot a graph of acceleration against displacement
Straight line through the origin
Negative gradient
Need to show A, -A, amax and -amax on the axes
What is the word for a system undergoing SMH with no resistive forces at play?
undamped
For an undamped system, describe the changes in KE and PE as the mass moves from the centre to the amplitude
At x = 0, V = max therefore KE = max, PE = min
At x = A, V = 0 therefore KE = 0, PE = max Loss of KE = Gain in PE
Explain how the height of a pendulum moved can be calculated using energy equations
KE=1/2m(vmax^2) at x = 0
PE=mgh at x = A
Loss from max KE = gain in PE
1/2m(v_max)^2=mgh (mass cancels out)
Describe the changes in KE of a undamped spring system in SMH
Kinetic energy
Bottom - KE is zero
Bottom to middle - KE increases to max at x = 0
Middle to top - KE falls to zero
Describe the changes in GPE of a undamped spring system in SMH
Gravitational potential energy
Bottom - GPE minimum
Bottom to middle - GPE increases
Middle to top - GPE increases to maximum
Describe the changes in elastic potential energy of a undamped spring system in SMH
Elastic potential energy
Bottom - EPE maximum
Bottom to middle - EPE falls
Middle to top - EPE falls to minimum
What is damping?
the removal of energy from a system in SMH
due to work done against resistive forces producing heat
What are the effects of damping?
Amplitude decreases
All types of energy (KE and PE) decrease
Maximum velocity decreases
Time period and frequency stay the SAME
For a damped system, describe the observed changes during one oscillation
Mass moves a shorter distance at a lower speed, but takes the same amount of time to complete the oscillation
What is used to measure whether something is decaying exponentially?
constant ratio property will be true at equal intervals
What is the constant ratio property?
ratio of current to previous amplitude after each complete oscillation
When will the natural frequency be observed?
when there are no external driving forces
When will a system oscillate at the driving frequency?
when there is an external driving force
Define resonance
if the driving frequency (f_d) is equal to the natural frequency (f_0) then resonance occurs where there is maximum energy transfer and the system oscillates with maximum amplitude
Describe the shape of a graph of amplitude to driving frequency
flat line with a narrow peak at a given driving frequency ( when it equals the natural frequency)
How will the shape of a graph of amplitude to driving frequency compare for a damped system?
same shape but lower amplitude for all frequencies (peak moves to the left slightly )
Use resonance to explain how microwave ovens work
Microwave produces a driving frequency = the natural frequency of water molecule vibrations
Resonance occurs and thus water molecules move with maximum amplitude and heat the food by transferring energy
Use resonance to explain why a tall building falls during an earthquake
A tall building oscillates with a natural frequency which is equal to the earthquake waves driving frequency
Resonance occurs and the building oscillates with maximum amplitude and thus collapses
How must you refer to a driving force in terms of applying it to observe resonance?
periodic driving force
In SHM, displacement is…
the distance moved by an object from its mean (or rest) position.
The time period of an oscillation is…
the time for one complete oscillation to take place at any point.
The frequency of an oscillation is…
the number of oscillations per unit time at any point.
The angular frequency of an oscillation is…
2π multiplied by the frequency and describes the angle moved in radians per unit time.
The phase difference is….
..the angle in radians between two oscillations. If the oscillations are in phase, the phase difference is 0 or a multiple of 2 π.
Forced oscillations…
…occur when a driving force acts on the object in order to keep it oscillating.
Free oscillations occur when…
…an object oscillates without a driving force . Objects undergoing free oscillations vibrate at their natural frequency.
