Spring problem

1. Aug 29, 2007

Yann

1. The problem statement, all variables and given/known data and 2. Relevant equations

Find position/velocity of a mass m attached to a spring of constant k when subjected to an oscillatinf roce

$$F(t) = F sin(Bt)$$

With $$B\not = \sqrt{k/m}$$

3. The attempt at a solution

Model;

$$mx'' + kx = F \sin(Bt)$$

I have no idea if/how it can be solved (without a computer, of course). Because;

$$mr^2 + k = 0$$

Gives

$$r = ±\sqrt{-k/m}$$

As $$B\not = \sqrt{k/m}$$ it can't be an answer.

2. Aug 29, 2007

Astronuc

Staff Emeritus
3. Aug 30, 2007

Yann

I'm not sure I understand your point, it's more a problem of math than a problem of physics, I must solve;

$$mx'' + kx = F \sin(Bt)$$

But I don't know how

4. Aug 30, 2007

learningphysics

First solve the homogenous equation first:

mx'' + kx = 0

Then you need a particular solution for
$$mx'' + kx = F \sin(Bt)$$

just plug in x = Asin(Bt) into the differential equation and solve for A...

Then your general solution is the solution for the homogenous equation + the particular solution Asin(Bt)...

And finally you need to deal with initial conditions...

5. Aug 30, 2007

Yann

Thx for the help, I solved the diff. equation. But will the solution to the differential equation give me the position or the velocity at time t ? And there's no initial condition, only $$B\not = \sqrt{k/m}$$, I don't know what to do with it.

6. Aug 30, 2007

Mindscrape

You actually need two boundary conditions, but since you don't have them you can probably just leave the two constants unsolved for.

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