3.6.1 Periodic Motion Flashcards
what is a radian
a unit for measuring angles
there are 2π radians in one full circle
what does motion in a circular path at constant speed imply
there is an acceleration and requires a centripetal force
what is the formula for the magnitude of angular speed
ω = v/r = 2π f
what is the formula for centripetal acceleration
a = v^2 /r = ω^2 r
what is the formula for centripetal force
F = m v^2 / r = m ω^2 r
in what direction is centripetal acceleration for circular motion
towards the centre (of the circle)
in what direction does the centripetal force act
towards the centre (of the circle)
what is simple harmonic motion
any motion in which the acceleration is directed towards a fixed point and is directly proportional to the negative of the displacement.
what is the equation for SHM
a = − ω^2 x
what are the characteristics of a displacement-acceleration graph
straight line graph
passes through the origin
what is the gradient of a displacement-acceleration graph
angular speed (angular frequency)
gradient = −ω^2
ω= (−gradient)^1/2
what is a damping force
any force which opposes the movement of the object
what is damping (in SHM)
when an oscillation is damped, the amplitude of the wave decreases, but the period and frequency remain the same
what is under-damping (light damping)
when the damping on a system is small and so the system is hardly affected. it will take a long time until the amplitude is seen to reduce or until the oscillations stop
what is over-damping (heavy damping)
if the system has too much damping, no oscillations will happen. so the object just slowly returns to equilibrium
what is critical-damping
if the object returns to equilibrium as quickly as possible
what is resonance
when a new frequency is applied to an oscillating system the amplitude of oscillation will change
what happens if the applied frequency is close to the natural frequency
resonance will occur and the amplitude will be at a maximum
what happens if the applied frequency is different from the natural frequency
the amplitude will be reduced to almost nothing
how does damping effect resonance (graphs)
the more damping the smaller the amplitude and the wider the resonance peak
when does resonance occur
when the driving frequency is equal to the natural frequency of the system
