Differential equation: Spring/Mass system of driven motion with damping

[TeenieBopper]

Homework Statement

A 32 pound weight stretches a spring 2 feet. The mass is then released from an initial position of 1 foot below the equilibrium position. The surrounding medium offers a damping force of 8 times the instantaneous velocity. Find the equation of motion if the mass is driven by an external force of 2cos(5t).

Homework Equations

F=kx
m=W/g

m\frac{d^{2}x}{dt^{2}}+\beta\frac{dx}{dt}+kx=f(t)

The Attempt at a Solution

I found that k=16\frac{lb}{ft} and m=1 slug. This gets me the following equation:

\frac{d^{2}x}{dt^{2}}+\beta\frac{dx}{dt}+16x=2cos(5t)

I'm at a loss for how to determine \beta, which is the damping force of 8 times the instantaneous velocity. I don't know how to determine instantaneous velocity. I know that once I have \beta, I can just use a LaPlace transform to find x(t). But \beta is my stumbling block right now.

As I was writing this, it occurred to me that \frac{dx}{dt}=instantaneous velocity and that would make \beta=8. That in turn makes the problem very easy to solve. Am I correct in this thinking?

We kind of rushed through this application in class the other day. Thanks in advance for any help you're able to provide.

 

[rock.freak667]

As I was writing this, it occurred to me that \frac{dx}{dt}=instantaneous velocity and that would make \beta=8. That in turn makes the problem very easy to solve. Am I correct in this thinking?.

Yeah I would agree that β=8 here. Just make sure your initial conditions are correct with the proper signs.