Calculating Velocity for Vibrating Beam System

[marcas3]

Homework Statement

The problem is as follows: there is a beam of length L pinned at both ends. A force F is acting in the middle. I must plot the velocity of this system at a point L/3 from the right. This is a continuous system so I am to use the pde approach.

Homework Equations

I'm pretty sure the equation below is the one to use. I know that plotting it will give me amplitude but how do I go about plotting the velocity? I'm thinking I just take the derivative of this equation since it gives me position. Is this a good assumption?

w(x,t) = ∑ [W_n (x) q_n (t)]

Any help greatly appreciated :)

 

[Valkarie]

The Attempt at a SolutionYes, you can take the derivative of this equation to get velocity. You simply have to differentiate both sides of the equation with respect to time. Doing so yields: w' (x,t) = ∑ [W_n' (x) q_n (t)] + ∑ [W_n (x) q_n' (t)]Now, you can substitute in your values for x and t, and use the boundary conditions to solve for the coefficients. Once you have the coefficients, you can plot the velocity at the point L/3 from the right.