# Equation of motion coursework

## 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..

#### Attachments

• cantelivered beam.png
5.8 KB · Views: 437

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)