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| Phy 340 page |
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| Sep 27 | Oct 25 | Nov 22 | ||
| Nov 29 |
29 Sep Talk about a homework problem, the one of finding how the roots of a quadratic equation move around as you vary one of the parameters.
Briefly recapitulate the solution of the damped simple harmonic
oscillator. What happens when there's an additional forcing term in the
equation? Use the property of linearity for this "inhomegeneous,
linear, ordinary" differential equation. You break the problem into
three steps:
The pendulum. Quickly set it up (a repeat of previous work). Show how to
get one integral of the equation by integrating dq. This is exactly the same as just writing down
the conservation of energy and using mgh for the gravitational
potential energy.
1 Oct
Harmonic oscillator hung from the ceiling. Show how the inhomogeous
solution just shifts the origin. The basis of the spring scale.
If I hold a mass suspended from a spring and move my hand up and down,
what is the response? Write the equation and again show how to guess
the solution. The distinctive difference in this case is that there is
a denominator that may vanish. What happens as the forcing
frequency becomes close to the natural frequency? Discuss this and
assign a homework problem to take the limit (having fixed some initial
conditions).
Go back to the forced, damped harmonic oscillator and show how to solve
it using complex exponentials.
2. Find and onesolution to the whole equation. This need not
have any arbitrary constants in it.
3. Add parts 1 and 2 to get the whole solution.
