# Equation of motion coursework

#### KateyLou

1. The problem statement, all variables and given/known data

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.

2. Relevant 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

3. 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..

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#### 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!

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