3.6.1 Periodic Motion

Question 1

what is a radian

Answer 1

a unit for measuring angles
there are 2π radians in one full circle

Question 2

what does motion in a circular path at constant speed imply

Answer 2

there is an acceleration and requires a centripetal force

Question 3

what is the formula for the magnitude of angular speed

Answer 3

ω = v/r = 2π f

Question 4

what is the formula for centripetal acceleration

Answer 4

a = v^2 /r = ω^2 r

Question 5

what is the formula for centripetal force

Answer 5

F = m v^2 / r = m ω^2 r

Question 6

in what direction is centripetal acceleration for circular motion

Answer 6

towards the centre (of the circle)

Question 7

in what direction does the centripetal force act

Answer 7

towards the centre (of the circle)

Question 8

what is simple harmonic motion

Answer 8

any motion in which the acceleration is directed towards a fixed point and is directly proportional to the negative of the displacement.

Question 9

what is the equation for SHM

Answer 9

a = − ω^2 x

Question 10

what are the characteristics of a displacement-acceleration graph

Answer 10

straight line graph
passes through the origin

Question 11

what is the gradient of a displacement-acceleration graph

Answer 11

angular speed (angular frequency)
gradient = −ω^2
ω= (−gradient)^1/2
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Question 12

what is a damping force

Answer 12

any force which opposes the movement of the object

Question 13

what is damping (in SHM)

Answer 13

when an oscillation is damped, the amplitude of the wave decreases, but the period and frequency remain the same

Question 14

what is under-damping (light damping)

Answer 14

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

Question 15

what is over-damping (heavy damping)

Answer 15

if the system has too much damping, no oscillations will happen. so the object just slowly returns to equilibrium

Question 16

what is critical-damping

Answer 16

if the object returns to equilibrium as quickly as possible

Question 17

what is resonance

Answer 17

when a new frequency is applied to an oscillating system the amplitude of oscillation will change

Question 18

what happens if the applied frequency is close tot he natural frequency

Answer 18

resonance will occur and the amplitude will be at a maximum

Question 19

what happens if the applied frequency is different from the natural frequency

Answer 19

the amplitude will be reduced to almost nothing

Question 20

how does damping effect resonance (graphs)

Answer 20

the more damping the smaller the amplitude and the wider the resonance peak

Question 21

when does resonance occur

Answer 21

when the driving frequency is equal to the natural frequency of the system