chapter 17 - oscillations Flashcards
what is formula for angular frequency , w ?
2 pi / T or 2 pi X frequency
define simple harmonic motion?
the acceleration is directly proportional to its displacement and acceleration acts opposite direction to displacement
what is formula for simple harmonic motion ?
a is proportional to -x
what does the graph of acceleration against displacement look like?
downward sloping through the origin
equation for velocity in simple harmonic motion?
v= w ( square root ( Amplitude^2 - displacement^2))
equation for maximum velocity?
v= w X Amplitude
what are the equations for displacement in simple harmonic motion?
x = A sin (w X t) or x = A cos (w X t)
use cosine when amplitude is at max at start
what is the phase difference of two pendulums when one is at max positive displacement and the other is at max negative displacement?
antiphase, phase difference of pi radians
what is the phase difference of two pendulums when both are at max positive displacement?
in phase , phase difference = 0
what is an isochronous oscillator?
it means that as amplitude increases time period remains the same, this is due to speed also increasing.
what are the two stores of energy in a simple harmonic motion?
the 2 stores are kinetic energy and potential energy (gravitational or elastic) with the sum at each displacement always equaling the total energy
formula for kinetic energy in simple harmonic motion?
1/2 X k (A^2 - x^2) where k is the force constant
what does the graph energy against displacement look like?
it is one U shaped curve with another inverted U curve on top with the peak of curves touching the total energy and 0 energy, they cross at exactly half total energy.
what is damping?
damping is when an external force acts on an oscillator reducing the amplitude of its oscillations.
when is damping used?
in bike suspension to absorb energy but maintain control.
what are the 3 forms of damping and give examples with pendulum?
light- pendulum oscillating in air
heavy - pendulum oscillating in water
very heavy - pendulum oscillating in thick oil
what is free oscillations and what is the frequency called?
free oscillations are when a mechanical system is displaced from its equilibrium position then allowed to oscillate without external forces. its frequency is the natural frequency.
what is forced oscillations and what is the frequency called?
this is when a periodic driver force is applied to an oscillator. the frequency is called the driving frequency.
what occurs when the driving frequency is equal to natural frequency?
the object will resonate, this results in dramatic increase of amplitude and if not damped the system will break
what is exponential decay?
exponential decay is when damping decrease amplitude by the same factor in equal time intervals.
what are uses of resonance?
- keep time in clocks using resonance of pendulum
- MRI scans
as amount of damping increase what occurs?
- amplitude decreases
- maximum amplitude occurs at lower frequency then natural frequency
- peak on graph of amplitude against frequency become flatter and broader.
For an object moving with SHM, what is the equilibrium position?
The midpoint of its motion
What is the displacement, x, of an object moving with SHM?
The distance and direction from the equilibrium position
What is the amplitude, A, of an object moving with SHM?
The maximum displacement from the equilibrium position
