V
DAMPER
k
M
kx
bv
Damped Oscillators
Consider the system pictured above. It looks like a normal mass on a spring
conguration, except for the motion damper (of drag constant b) attached
to the right side of the apparatus.
Fx = max
d2 x
kx bvx = m 2
dt
d2
Oscillations: Two General Approaches
Someone hands you a system that oscillates, and asks you to nd the equation
of motion. What are you going to do? Well, here are two methods that I nd
useful for solving these things:
Forces
Draw a picture of the syste
Taylor Series
The Taylor Series expansion of f (x) for points near x = a can be written:
f (x) =
n=0
1 ( n)
f (a) (x a)n
n!
Expand through the rst few terms and take some derivatives. . .
f (x) = f (a) + f (a) (xa) +
1
1
1
f (a) (xa)2 + f (a) (xa)3 + f
1B Midterm review
4/15/2016
Jiming Sheng
Note
The focus on this review session is problem solving, and the formulae
and concepts listed in the slide is not exhaustive. Please also study the
textbook and lecture notes for better effect.
Making the correc