How to Find the Equation of Motion for a Cantilevered Bar with a Damper?

[KateyLou]

Homework Statement

I have coursework on rhe convolution integral, however i am struggling to find the equation of motion to start the whole thing off with.

I will attach a picture of the problem, is is simply a cantilevered bar with a concentrated mass on the end and a damper.

Homework Equations

I am assuming you find the deflection at the end of the beam as a result of the force P(t), which i think is
P(t)L^3/3EI

However i am not sure where to go from here

The Attempt at a Solution

Thinking it may possibly be
m\ddot{x}+c\dot{x}=P(t)L^3/3EI
however i think i may need to add in stiffness somewhere else..

 

[Dr.D]

Your simple model for the cantilever, looks OK, and it gives you the stiffness if you look at it properly. You have a deflection relation that is usually written as
defl = P*L^3/(3*E*I)
Now re-arrange that to read
P = (3*E*I)/(L^3) * defl
and from there you can see that the stiffness of this system is
K = 3EI/L^3
Now back to your equation of motion, which will look like
m*xddot + c*xdot + K*x = F(t)
where F(t) is whatever applied forcing function acts on the mass.

See if that will get you going!