Brownian Motion, Mean Square Value

[CharmedQuark]

I'm not sure where this belongs but I figure that this is the right place for it.

Homework Statement

The equation is m*v'(t)+$$\mu$$*v(t)=f(t), where m is mass, $$\mu$$ is the drag coefficient, and f(t) is some random function. I am asked to find the values for v(t), <v²>, and <x²>

Homework Equations

Uhh...

The Attempt at a Solution

Okay the first part is an easy DE for which I got v(t) I got v(t)=Ce^-$$\mu$$t/m+(e^-$$\mu$$t/m)/m*$$\int$$e^$$\mu$$t/mf(t)dt, where C is an arbitrary constant. I have no idea how to go about finding the other two answers. I am supposed to find them analytically but I am not sure how to go about this. Any help is greatly appreciated.

 

[kurt.physics]

The solution to the first part is correct, and the other two values can be found by using the equation for v(t). To find <v2>, you need to integrate v(t)^2 from t=0 to t=T, where T is the final time. To find <x2>, you need to integrate x(t)^2 from t=0 to t=T. If f(t) is not known, you can't solve this problem analytically.