Understanding Governing Differential Equations in Mechanics
School
University of British Columbia**We aren't endorsed by this school
Course
MATH 345 345
Subject
Mechanical Engineering
Date
Dec 11, 2024
Pages
3
Uploaded by JudgeGalaxyMeerkat35
MECH 330 — Fall 2024 Assignment #2 Due Sep 27, 23:59 Problems 1-2: Using the generalized coordinate shown, find the governing differential equation of motion by applying Newton’s Law. A—w—F Slender bar of mass m W | N W | I —] s 3 7 —> x (I —— Rigid S massless k link ANV =1l Ll L 3 Thin disk of mass m, J_ no slip Problem 1
Note: In problem 2, the governing differential equation can be represented in nonlinear form. Sphere of mass m, radius 7, no slip Problem 2
Problem 3: The uniform rigid bar AB with mass m is supported by the linear springs &, and k,, and also the torsional spring £, at point A. The system is in equilibrium when the bar is horizontal. Find the equation of motion and natural frequency of the system. N k! kl e E————— .B - \ A Q - a i > k2 N - ! ;! Problem 3 Problem 4: Derive an expression for the displacement of the system in Problem 3 (in terms of the coordinate ©) as a function of time when: a) the system is displaced by 10 degrees and then released. Draw a graph of the response (6(t)). b) an initial velocity of 2 m/sec is given at point B. Draw a graph of the response (O(t)).