assigned today:

Due today:

- standard-Laplace transforms:
I can use Laplace transforms to solve differential equations.

- Compare and contrast the Laplace transform and eigensystem approach to second order differential equations with constant coefficients.
- Any problems from chapter 6 review 29-33.
- For a spring system with m=1, viscosity=2, and k=10, determine a plot of the trajectory of the system if x(0)=x'(0)=0 and the driving function is 2 from t=0 to t=1, -2 from t=2 to t=3 and zero otherwise. Use a convolution approach.

Due today:

- Quiz on damped SHO using series solution
- interesting that while a1 was zero, the other odds weren't

- Asked what they knew of Laplace transforms
- should make equations easier
- some took a stab at what the transformation was
- some said to look them up in a table

- Talked about linearity
- had them derive the results for \(\mathcal{L}[f'(t)]\) and \(\mathcal{L}[f''(t)]\)
- Had them go through the 4 steps for a damped, driven oscillator

$$y(t)=\mathcal{L}^{-1}\left[\frac{R(s)}{a s^2+bs+c}\right]$$

- Talked about how step 4 is the tough one usually and how all the problems in the book are made such that it's possible
- talked about how convolution can get around step 4 at the cost of a new integral to do