Resonance and Damping Flashcards
what two types of oscillations are there
free and forced oscillations
when do free oscillations happen
- when a system performs oscillations
- free from the influence of any forces from outside the system
what is a natural frequency
- the frequency any oscillating system naturally chooses to oscillate at
- when left alone to freely oscillate
how could you change the free oscillation of the pendulum into a forced oscillation
- by externally exerting a force on the pendulum
- such as pushing the bob in the opposite direction its naturally oscillating to
what is the name of the frequency you have now forced the pendulum to oscillate at
- the driving frequency
- specifically your driving frequency
what is resonance
- a phenomenon which describes very large amplitude oscillations that occur
- when a driving frequency matches the natural frequency of the system
why does the amplitude of an oscillation become very large during resonance
- because the system is absorbing the extra energy from the driving frequency
- this added to its natural frequency leads the increase of its amplitude
what is going on inside a washing machine that causes it to sometimes be loud or quiet
- when loud the motor would be spinning at the same natural frequency of one of the panels
- this resonance results in large amplitudes which therefore results in loud noises
- when quiet the motors rotation generates vibrations at other frequencies that dont match the natural frequency of any part of the machine
what will a graph of vibrational amplitude against frequency show for the washing machine example
- the line will be very shallow (at 0 basically) and have a very low gradient for most of the frequencies
- then it will begin to steeply rise and peak quickly
- only to quickly fall back down to low levels but be slightly higher than before
- with some sort of turbulence following the line
what is the peak of that graph telling you
- the frequency at which resonance occurs
- and therefore the natural frequency of the panel
there is a mass on a spring connected to a vibration generator connected to a signal generator. the mass on the spring is above a motion sensor that is connected to a computer that datalogs the height of the mass. what is the equation for the time period of the oscillation of the mass on a spring
T = 2pi * root of (m / k)
what do each of those variables mean
- T= time period per oscillation
- m = mass of mass on spring
- k = spring constant
given that is the equation for time period, what is the equation for frequency and why
- f = (1 / 2pi) * root of (k / m)
- because T = 1 / f
what is the specific name of this frequency
the resonant frequency
what does measuring the amplitude of forced oscillations allow us to find and why
- the resonant (natural) frequency
- because the forced oscillations are created from the driving frequency of the vibration generator
- and this is in resonance with the natural frequency
how would we rearrange this equation to work out the mass
- f^2 = (1 / 4pi^2) *( k / m)
- f^2 = k / 4pi^2 m
- m = k / 4pi^2 f^2
therefore what is the equation for working out the spring constant
k = 4pi^2 f^2 m
what are damped oscillations
- oscillations which suffer a loss in energy each time they oscillate
- reducing their amplitude each time
if a system is performing simple harmonic motion at its natural frequency, what two things could practically cause the dissipation of energy in that system
- a frictional force acting on the system
- or the plastic deformation of a ductile material in the system
what is damping
the material or system causing an energy loss each damped oscillation
what is an example of damping in a swinging pendulum
air resistance
despite the amplitude of oscillations decreasing overtime, what still remains constant throughout
the time period for each oscillation
what does it mean if a system is critically damped
- damping occurs such that the oscillator returns to its equilibrium position in the quickest possible time
- without going past that equilibrium position
what would critical damping look like on a displacement-time graph
- the line would start on the top of the displacement axis
- then gently plateau onto the time axis and rest on it
what is overdamping
- when the system has been damped too much
- causing the oscillator to take a very long time to return to its equilibrium position
where is overdamping practically used
in car suspension systems
what would overdamping look like on a displacement-time graph
- the line would start at the top of the displacement axis
- then gently begin to plateau similar to the critical damping line
- but it would stake significantly longer for it to reach the time axis
- on most graphs it doesnt even reach it, its just left there suspended in the air
what would a normally damped (underdamped) line look like on a displacement-time graph
- the line would start at the equilibrium position and begin to oscillate normally
- but with each full oscillation the peaks become smaller
- until the line is just hugging the time axis with minuscule amplitudes
what would an undamped line look like on a displacement-time graph
like any other normal oscillation, having constant amplitudes
what is the goal for most engineers when creating a damping system for an object
to create a good medium between underdamping, critical damping and severe overdamping
what is a main issue engineers come across when trying to achieve this
one object can have multiple natural frequencies
what kind of damping would we want a shock absorption system to have and why
- critical damping
- because we want to make sure the system returns to equilibrium without overshooting
- thereby stopping the oscillations as quickly as possble
how do opera singers break wine glasses with their voice
- they sing at a pitch that matches the natural frequency of the wine glass
- this causes resonance to occur within the wine glass
- the very large amplitudes caused by resonance rattle the structure of the glass so much that it breaks
what two properties do climbing ropes need to have and why
- they need to be stretchy to avoid a sudden and painful stop to a fall
- but they need to be stiff enough to bring the climber to a halt
how is this balance created in a climbing rope
- the rope consists of several woven strands
- there is a ratio of stretchy strands to stiff strands which make the ideal balance between a stretchy and stiff rope
