Equation of motion coursework

[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!

 

[Mene]

I would suggest starting by reviewing the fundamental principles and equations of motion for a cantilevered beam with a concentrated mass and a damper. This may include equations for static equilibrium, moment and force balances, and the relationship between deflection, stress, and strain. Once you have a solid understanding of these principles, you can then apply them to the given problem and use the convolution integral to solve for the equation of motion.

Additionally, it may be helpful to break down the problem into smaller, simpler components and solve them individually before combining them into the final solution. You may also want to consult with your instructor or classmates for clarification or assistance in understanding the problem.

Remember to always approach coursework with a critical and analytical mindset, and don't be afraid to ask questions and seek help when needed. Good luck with your coursework!