-kx
F
0
x
m
k
a
m
k
ω
2
π
ω = 2 π f
=
T
T
1
f
δ)
ωt
(
sin
A
x
δ)
ωt
(
cos
ω
A
v
2
a = -A
ω
sin ( ωt +δ)
0
x
ω
a
2
A=x
max
max
v
= A
ω
2
max
a
= A
ω
spring SHM
11-0
L
g
ω
Pendulum

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Examples: Spring, Pendulum…
Most mechanical systems- displace from equilibrium- 2 possibilities
restoring force 1
st
approx F=-kx
oscillates about equilibrium
with natural frequency
repulsive force - runs away
Small displacement Simple Harmonic Motion Dynamics
potential energy 1
st
approx
U=1/2 kx
2
3 Points to note
hit (tickle) system
–
it “rings” at a natural frequency (f
o
)
vibrate
system with frequency (f)- it responds with f but close
to (or at) f
o
get sharp, big “resonant” response
friction makes natural ring die of exponentially with time
11-1