# Vibration of a cantilever beam

1. Jun 5, 2017

### Feodalherren

1. The problem statement, all variables and given/known data
A rectangular cantilever beam of length L and side lengths b with negligible mass is attached horizontally to a wall. A mass m is attached to the end of the beam where a motor is also located. The motor applies a force on the end of the beam described by the equation P*sin(w*t).

Derive an expression for the vertical vibration of the mass m, that is, find x(t) for a stable solution.

2. Relevant equations
k = 3EI / L^3
I = b^4/12

3. The attempt at a solution
I'm at a loss here. I am unaware of any equation that describes the damping in a cantilever beam. I want to set up the problem as

x'' + c/m x' + k/m x = Psin(wt)/m

which is how I usually solve these types of problems. But I'm at a loss when it comes to finding out how to express c. Furthermore, when it says to find a stable solution, is it hinting towards harmonic motion?

2. Jun 5, 2017

### Feodalherren

Perhaps they mean that it is simple harmonic motion without damping?

3. Jun 5, 2017

### haruspex

Yes, it is forced, undamped.