Equation of motion coursework

• KateyLou
In summary, the conversation discusses a coursework on the convolution integral and finding the equation of motion for a cantilevered bar with a concentrated mass and a damper. The suggested deflection relation is defl = P*L^3/(3*E*I), which can be rearranged to find the stiffness of the system. The equation of motion is then given as m*xddot + c*xdot + K*x = F(t), where F(t) is the applied forcing function.
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..

Attachments

• cantelivered beam.png
3.5 KB · Views: 501
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)
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!

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!

1. What is the equation of motion?

The equation of motion is a mathematical representation of the relationship between an object's position, velocity, and acceleration over time. It is commonly expressed as s = ut + 1/2at^2, where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time.

2. How is the equation of motion used in coursework?

The equation of motion is often used in coursework to solve problems involving the motion of objects. By plugging in known values for displacement, initial velocity, acceleration, and time, students can calculate unknown values and analyze the motion of an object.

3. What are the three types of equations of motion?

The three types of equations of motion are the first, second, and third equations. The first equation relates displacement, initial velocity, acceleration, and time. The second equation relates final velocity, initial velocity, acceleration, and displacement. The third equation relates final velocity, initial velocity, acceleration, and time.

4. Can the equation of motion be used for all types of motion?

No, the equation of motion can only be used for motion with constant acceleration. This means that the velocity and acceleration of the object must be consistent throughout the motion. For motion with changing acceleration, more complex equations are needed.

5. How can the equation of motion be applied in real-life situations?

The equation of motion can be applied in real-life situations to predict the motion of objects, such as projectiles or vehicles. It can also be used to analyze the motion of natural phenomena, such as free-falling objects or planetary orbits. Additionally, the equation of motion is used in fields such as engineering and physics to design and improve various systems and structures.

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