further mechanics - simple harmonic motion Flashcards
what are the 2 conditions for simple harmonic motion?
acceleration is proportional to displacement.
acceleration is in the opposite direction to displacement.
what is the restoring force in a simple pendulul?
gravity
what is the restoring force in a mass spring system
elastic force
total energy of a system =
potential energy (gravitational or elastic) + kinetic energy
at what point is potential energy at a maximum? when is it at a minimum?
max potential energy at maximum displacement (far left/right in a simple pendulum, at maximum extension/compression for mass spring system)
minimum potential energy at the midpoint
when is kinetic energy of a system at a maximum? when is it minimum?
maximum at midpoint
minimum (0) at max displacement
how can you convert between displacement (x) velocity (v) and acceleration (a)
v = x’
a = v’= x’’
what approximation do you use to be able to derive and equation for the time period of a simple pendulum? what are the conditions for this?
small angle approximation
sin(x) ~ x
x<10
what are free oscillations?
when a system oscillates without damping (so amplitude remains constant)
what is light damping?
the system oscillates with decreasing amplitude
what is heavy/over damping?
the system has so much damping that kt returns to its equilibrium position without oscilating
is critical damping?
the system returns to its equilibrium position in the shortest possible time without oscillating
if an oscillating system is damped (eg light damping from air resistance) how can the oscillations be maintained?
energy must be supplied by a perioding driving force
if a system is oscillating due to a periodic driving force, what type of oscillations are happening?
forced oscillations
what is the name for the frequency of a freely oscillating system?
natural frequency
when a system oscillates with forced oscillations, what is the amplitude of the oscillations dependant on?
the frequency of the periodic driving force
what is resonance?
if the frequency of a periodic driving force is the same as the natural frequency of a system, the amplitude of the system reaches a maximum.
if f < < natural frequency…
the system will oscillate approximately in phase with the driving force at a similar amplitude to that of the driving force
if f = natural frequency….
system oscillates approximately 90 degrees out of phase with the periodic driving force with a maximum amplitude
if f > > natural frequency…
the system oscillates approximately 180 degrees out of phase with the periodic driving force and with a very small amplitude.
why does amplitude decrease when as system is damped?
system loses energy as work is done against the damping.
if a forced oscillating system is damped, what happens to the maximum amplitude where resonance occurs?
maxima becomes less pronounced, and the frequency at which resonance occurs decreases.
