# Homework Help: Forced oscillation

1. Mar 17, 2012

### Lizwi

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

F= ma= -kx -bv + Fext where k and v are spring constant and velocity respectively and Fext is an additional external force.

2. Relevant equations
I know how to solve nonhomogeneous differential equations mathematically but on the right of the above equation is not a function so I stuck.

3. The attempt at a solution

I tried this way:
writing the above as differential equation I have
md2x/dt2 + bdx/dt + kx = Fext
for homogeneous part md2x/dt2 + bdx/dt + kx=0
the solution I assumed is x(t) =Aept
the first derivative of the assumed solution is x'(t)= Apept and the second derivative is x''(t)= Ap2ept
substituting all these x(t), x'(t) and x''(t) to the differential equation and devide by
Aept I get:

mp2 + bp+k=0
for inhomogeneous part I don't know ho to handle this right hand side Fext. Please help me.

Last edited: Mar 17, 2012
2. Mar 17, 2012

### tiny-tim

Hi Lizwi!
Is Fext a constant?

You need to find any solution for the whole equation …

try polynomials first (starting with constants!)

3. Mar 18, 2012

### rude man

You need to know the explicit expression for your driving function first, so you can "guess" at the inhomogeneous solution. What is it?

4. Mar 18, 2012

### OldEngr63

You could express the solution for any right side function by means of a convolution integral, but that is only a symbolic solution and not good for too much.

5. Mar 18, 2012

### sgd37

just absorb the external force into x i.e. x' = x + F. If it's a constant then it's not too difficult to solve, if it isn't then you have another (manageable) diff equation to solve.