Lecture 23
pls23.1
Harmonic Oscillations
Media: 1.
Wooden block (and several weights) on spring / string
2.
Equipment to measure oscillating block
3.
Fendt circular motion demo
1.
Ideal Spring
The idealspring force is expressed as
(
)
eq
x
sp
x
x
k
F
−
−
=
,
where
k
is known as the spring constant
of the spring.
x
+
x
sp
F
,
eq
x
equilibrium position of the end of the spring.
x
sp
F
,
x
sp
F
,
eq
x
x
−
eq
x
x
−
eq
x
x
−
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Lecture 23
pls23.2
Note:
(i)
Larger
k
Æ
stronger spring.
(ii)
Minus sign is because
x
sp
F
,
is in direction opposite to
eq
x
x
−
.
(iii)
eq
x
x
−
can be either
+
or
−
(and
x
sp
F
,
has opposite sign).
2.
Harmonic Motion
Demo:
measure motion of oscillating block
Motion looks harmonic
(sine or cosine).
Clicker questions 1
.
Demo with different amplitude
Clicker questions 2
.
Demo with different mass
If we start the oscillations with an initial displacement
A
and no initial
velocity, then its displacement vs time can be written as
( )
(
)
t
A
x
t
x
eq
ω
cos
=
−
T
f
π
π
ω
2
2
=
=
Assume no friction, no drag
eq
x
sp
F
sp
F
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 Fall '11
 KODERA
 Physics, Circular Motion, Force, Simple Harmonic Motion, Wnc, Xeq

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