Transcript Thought for the Day

Thought for the Day
Midterm
Friday October 26, 5–7pm
room to be determined
one person writing early (must email me
today)
Tutorials/TAs
Tutorials
 T0101: M 10am, MP 134
 T0201: T 10 am, MP 137
Teaching Assistant
Jean-Sébastien Bernier
Study groups
if you’d like help to find others wanting to
form study groups, send me an email
LIKE THIS:
 Subject: ABC PHY255 study
 no content in the body
I’ll send out an email to those people,
with all people’s addresses in the To: field
(in the clear)
Modelling oscillations
Elements of an oscillator
need inertia, or its equivalent
 mass, for linear motion
 moment of inertia, for rotational motion
 inductance, e.g., for electrical circuit
need a displacement, or its equivalent
 amplitude (position, voltage, pressure, etc.)
need a negative feedback to counter inertia
 displacement-dependent restoring force: spring,
gravity, etc.
 electrical potential restoring charges
Hooke’s Law
restoring force proportional to
displacement from equilibrium
F kx
x
m m
Oscillation of mass on spring
restoring force
inertial force
equation of motion
F(t)kx(t)
F(t) ma(t) mxÝ
(t)
Ý
mxÝ
(t) kx(t)
Ý
x(t) is a function describing the oscillation
what function gives itself back after twice
differentiated, with negative constant?
cos(at), sin(at) both do work
exp(at) looks like it ought to work...
Oscillation of mass on spring
mxÝ
(t) kx(t)
Ý
try: x(t) Asin(w tfo)
m{Aw 2sin(w tfo)}kAsin(w tfo)
w 2  k/m
frequency determined by spring constant k,
and by mass m.
cos(wt+fo) is similar
Phasor notation
mxÝ
(t) kx(t)
Ý
try: x(t) Aexp(atfo)
m{Aa2 exp(atfo)}kAexp(atfo)
2
a  k/m
a  1 k / m  iw
x(t)=Aexp(iwt+fo) is a solution also