Damped harmonic oscillator Diff. Eq. question

1. Mar 17, 2016

Dusty912

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. Mar 17, 2016

Buzz Bloom

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.

Regards,
Buzz

3. Mar 17, 2016

Dusty912

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.

4. Mar 17, 2016

Dusty912

Im just not sure what the question is seeking as far as written work

5. Mar 17, 2016

Buzz Bloom

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?

Regards,
Buzz

6. Mar 17, 2016

Dusty912

Well by plugging it in. Correct?

7. Mar 17, 2016

Buzz Bloom

Hi Dusty:

What do you get when you plug it in?

Regards,
Buzz

8. Mar 17, 2016

Dusty912

cm d(y(t))/dt2 +bc d(y(t))/dt +kcy(t)=0

9. Mar 17, 2016

Buzz Bloom

Hi Dusty:

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

Regards,
Buzz

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