Oscillations Flashcards
displacement
the distance from the oscillator to the equilibrium
amplitude
max displacement to the equilibrium
time period
the time it takes to complete one full oscillation
Frequency
the number of oscillations per unit time
angular frequency, w
the rate of change of angular displacement
what is the equation that relates angular frequency and time period
w = 2Pi/T
what are the conditions fro simple harmonic motion
acceleration must be directly proportional to the displacement and in the opposite direction
it must act towards the equilibrium position
two main examples of systems which undergo simple harmonic motion
spring and a pendulum
when is velocity minimum
at the amplitude of an oscillation
why is the velocity minimum at the amplitude of an oscillation
as the object changes direction
when is velocity maximum
when the object passes through the equilibrium position
how do you calculate maximum speed
Vmax = wA
draw a graph for the potential energy and kinetic energy against displacement for a simple harmonic system
what is damping
process by which the amplitude of the oscillations decreases over time. this is due to energy loss to resistive forces such as drag or friction
what happens with light damping
> it occurs naturally
amplitude decreases exponentially
time period remains the same as A and T are independent
what happens when heavy damping occurs
the amplitude decreases dramatically
what happens during critical damping
object is stopped in as short time as possible without overshooting the equilibrium
free oscillation
system is disturbed initially and then oscillates with no external force, it oscillates at its natural frequency
forced oscillation
driving force is applied to an object which causes it to oscillate at a particular frequency
what is resonance
when the driving force of the external force applied to an object is the same as the natural frequency of the object
what happens when resonance occurs
> amplitude of oscillation rapidly increases and if there is no damping the amplitude will continue to increase until the system fails
as damping is increases the amplitude will decreases at all frequencies and the maximum amplitude will occur at a lower frequency
experiment to investigate the resonance of an object
> suspend mass between two springs attached to oscillation generator and use a ruler parallel with the spring mass system to record the amplitude
increase the frequency of the generator slowly so that the amplitude increases, reaching maximum amplitude when the driver frequency is the same as the natural frequency
since drag due to air damps the system the amplitude should not continue to increase until the point of system failure
to increase accuracy system can be filmed and the amplitude recorded from video stills
experiment to determine the period and frequency
> add a mass to the end of a spring which is attached to a stand then place a fiducial marker in line with the mass
displace the mass, to initiate simple harmonic motion
measure 10T from equilibrium position with the use of fiducial marker
take all measurements from eye level to reduce parallax error
divide by 10 to get time period
and if want frequency, frequency = 1/T
take multiple measurements and find the mean to improve accuracy
what is the name given when the period of a simple harmonic oscillator is independent of the amplitude
isochronous oscillator
how can you find the velocity at a given time
find the gradient
when does maximum kinetic energy occur
at the equilibrium position as this is where the velocity is at its maximum
where does maximum potential energy occur
at the amplitude as this is where displacement is at its maximum and total energy is conserved
