Oscillations & waves
[Pages:30]oscillations & waves
physics 111N
periodic motion
! often a physical system will repeat the same motion over and over ! we call this periodic motion, or an oscillation the time it takes for the motion to complete one cycle is called the period, T the number of times the motion repeats in unit time is called the frequency, f
so e.g. if the period is 0.1 s, the frequency is 10 s-1
physics 111N
2
simple harmonic motion
! a very special form of periodic motion where the restoring force is proportional to the displacement
! once way to construct such an oscillator is to use a spring obeying Hooke's law
spring compressed
spring at equilibrium
spring extended
physics 111N
x F
x F
x F
4
simple harmonic motion
! a very special form of periodic motion where the restoring force is proportional to the displacement
! once way to construct such an oscillator is to use a spring obeying Hooke's law
physics 111N
5
simple harmonic motion
x=-A
the amplitude of motion, A, is the maximum displacement from equilibrium
physics 111N
6
simple harmonic motion
0
0
3T4
T4
T2
0
a v
x F
xA x0 xA x=-A
3T4
T4
T2
0
a v
x F
xA x0 xA x=-A
3T4
T4
T2
0
F xA x=-A
a v x
x0 xA
3T4
T4
T2
0
a v x
xA x0 x=-A
F xA
3T4
T4
T2
0
a v x F
xA x0 xA x=-A
3T4
T4
T2
0
xA x=-A
a v x F
x0 xA
3T4
T4
3T4
T4
T2
a
v
x
F
T2
a
v
x
F
physics 111N
xx=-AA x0 xA
xx=-AA x0 xA
7
energy in simple harmonic motion
! the elastic restoring force is conservative & there is no friction, so total energy is conserved
when x=A, the block is at rest
x=-A
physics 111N
8
energy in simple harmonic motion
! the elastic restoring force is conservative & there is no friction, so total energy is conserved
@
physics 111N
9
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