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Homework 2

Prof. Daniel H. Cortes
ME 370
Spring 2022
Homework 2: Due Monday 2/7/2022 by 1:25pm by Canvas PDF Submission
Homework Policy (See Syllabus for full details):
Homework must be submitted electronically by each student as a single PDF file containing all
problems and work to the corresponding Canvas website Homework Assignment.
Homework must show all work. If you use MATLAB, submit your code as well as the output.
Homework will be accepted until the submission deadline indicated on Canvas. Late submissions are
accepted at a penalty.
You may work in groups, but you must be able to completely explain everything you turn in. Simply
copying a solution, or part of a solution, is not acceptable and is a breach of academic integrity.
Similarly, any MATLAB code you submit should be distinct; your entire study group should not submit
identical code.
1. Determine the equivalent mass and the equivalent stiffness of the following mechanism. Consider
small rotations of the bar. Hint: you may treat this mechanism as a 1 DOF system with an
equivalent torsional spring and an equivalent moment of inertia.
2. Find the equivalent damping 𝑐𝑒𝑞 of the following system of dampers connected to a rigid bar.
Express as 𝐹 = 𝑐𝑒𝑞 𝑣 = 𝑐𝑒𝑞 𝑥̇.
Prof. Daniel H. Cortes
ME 370
Spring 2022
3. Determine the equivalent stiffness.
4. Draw the FBD and derive the EOM of the pulley system below with respect to x using Newton’s
laws. Mass 𝑚 slides on a rough surface with friction force 𝑓. Hint: the tension of the cable
connecting the mass and the pulley can be obtained by analyzing the FBD of the mass m.
5. An engineering team is designing a food delivery robot. The robot has two wheels and a rigid
body of mass 𝑚𝑤 and 𝑚𝑏, respectively. The wheel has a radius 𝑅 and spins at angular velocity 𝜔.
Find the equivalent mass of the robot. Assume that the wheels do not slip on the ground, are
moving at the same speed and that the axle connecting the two wheels has negligible mass.
Write out the equation of motion based on the equivalent translating system.
Prof. Daniel H. Cortes
ME 370
Spring 2022
Find the equation of motion for the small rotations of the system composed of a rigid bar of length
𝑙 pinned at point O. The rigid bar mass is m.