math285, week of october 13

Read the textbook, chapters 3.4 and 3.6. additional reading (highly recommended).

Videos to watch.

Homework (due by Tuesday, 10.21):

    Solve using variation of parameters:

  1. \[
    y”+9y=\sec(3t);
    \]
    Answer:\((1/9)\cos(3t)\ln|\cos(3t)|+(1/3)t\sin(3t)+C_1\cos(3t)+C_2\sin(3t)\).
  2. \[
    y”+2y’+y=e^{-t}/t.
    \]
    Answer: \(e^{-t}t\ln{t}+C_1e^{-t}+C_2te^{-t}\).
  3. Consider a mass \(m=1\) on a spring with spring constant \(k=4\) oscillating on a surface with the damping constant \(c\).Sketch the trajectories of the motion of a mass starting position \(0\) with velocity \(1\) for \(c=0, .1, 3, 5\).

 

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