Derive a differential equation relating the input and force

Assignment Help Simulation in MATLAB

Reference no: EM132374788

Motion Control Assignment - Modeling Dynamic Systems using Differential Equations

Note: Print out this problem sheet and attach your solution sheets to this problem sheet. Staple them and turn in. Remember to follow and show the modeling steps.

Problem 1: a) Derive a differential equation relating the input, force f(t), with the output, displacement x(t), for the system described by the following figure. (A dashpot/viscous damper and a spring connected to a mass with external force f(t) as input)

b) If damping coefficient fv = 2 N-s/m, spring constant K = 9 N/m, and mass of object m = 1kg, plug them into derived differential equation, and rewrite the differential equation.

Problem 2: The wheel of diameter D rotates on its axis as shown. The moment of inertia of the disk about the axis of rotation is J. Two linear springs with spring constant K are attached at the outer diameter as shown, such that the springs compress or extent when the wheel rotates. An external torque T(t) acts on the wheel. There is no damping. Derive a differential equation relating the input torque T to the angular displacement θ as a function of time. You can assume that θ is small.

Problem 3: A non-linear spring can be described by F = x+0.1*x^3. Determine a linearization for the spring about the points x=1 and x=3 as shown in the figures. i.e. determine the slope of the red dashed line. You must show your work. (Hint: the answer to one of the problems is F = 3.66x).

Problem 4: A robot arm rotate in the XY plane as shown below (horizontal plane, i.e. gravity acts in Z direction). The motor applies a torque T to the arm. Assume a viscous damping torque with coefficient D. Derive a differential equation relating the input, torque T, with the output, angular displacement θ.

Reference no: EM132374788

Questions Cloud

Have you ever managed or followed in a path goal style : Have you ever managed or followed in a Path Goal style? What were the circumstances, and was it effective? Why or why not?

Why did skynet declare war on the human race : Describe Digital Literacy. Why did Skynet declare war on the human race? What are some drawbacks to crowd sourced answers?

Advantage of using cloud base software service : What is the advantage of using cloud base software service?

Primary differences between wi-fi and wimax : How can you Identify the primary differences between Wi-Fi and WiMax.

Derive a differential equation relating the input and force : MET 4052 - Motion Control Assignment - Modeling Dynamic Systems using Differential Equations, University of Cincinnati, USA

How does it differ from e-business : What is e-commerce? How does it differ from e-business? Where does it intersect with e-business?

Managing social responsibilities and ethical issues : Details of the dilemma along with a detailed recommendation on how the organization should proceed will be highly appreciated.

Time required for speedy lube finish : The time required for Speedy Lube finish an oil change service on an automobile approximately follows a normal distribution, with mean of 17 minutes

Using sampling to reduce the number of data objects : Discuss the advantages and disadvantages of using sampling to reduce the number of data objects that need to be displayed.

Reviews

len2374788

9/23/2019 2:25:07 AM

Instructions: For problem 3 and 4 Need to be done on Matlab and these problems are related to HW 2. Need everything done on MO office including the Matlab code that is related to problems 3 and 4 It is HW 3 but I will attach HW 2 to help you if you need any information for problem 3 and 4. Note: Print out this problem sheet and attach your solution sheets to this problem sheet. Staple them and turn in. Remember to follow and show the modeling steps.

Write a Review

Required(*) Message

User Account

All Pages