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Damped harmonic oscillator Diff. Eq. question

  1. Mar 17, 2016 #1
    1. The problem statement, all variables and given/known data
    consider any damped harmonic oscillator equation

    m(d2t/dt2 +bdy/dt +ky=0

    a. show that a constant multiple of any solution is another solution
    b. illustrate this fact using the equation
    (d2t/dt2 +3dy/dt +2y=0

    c. how many solutions to the equation do you get uf you use this observatiob along with duess-and-test method described in this section?
    2. Relevant equations
    guess-and-test method. subbing est for y, and then solving for s value to obtain two solutions

    3. The attempt at a solution
    now I know for (a) I am supposed to sub in ky(t) into the damped harmonic oscillator. but I am stuck from there. I am not really sure what kind of answer this question is looking for. Any help would be appreciated.
  2. jcsd
  3. Mar 17, 2016 #2
    H i Dusty:

    If you assume y(t) is a solution, what do you think "a constant multiple of any solution is another solution" means?

    Hope this helps.

  4. Mar 17, 2016 #3
    well I believe it means that if y(t) is a solution then ky(t) is also a solution. Where k is an arbitrary constant.
  5. Mar 17, 2016 #4
    Im just not sure what the question is seeking as far as written work
  6. Mar 17, 2016 #5
    Hi Dusty:

    I would avoid using k as the "constant" used in the "constant multiple", since k appears in the equation. For example try cy(t) instead.
    How would you show that cy(t) satisfies the DE?

  7. Mar 17, 2016 #6
    Well by plugging it in. Correct?
  8. Mar 17, 2016 #7
    Hi Dusty:

    What do you get when you plug it in?

  9. Mar 17, 2016 #8
    cm d(y(t))/dt2 +bc d(y(t))/dt +kcy(t)=0
  10. Mar 17, 2016 #9
    Hi Dusty:

    Right. What do you get if you divide this equation by c? What does that tell you?

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