ME-GY 5443 Make Up Exam 1 Fall 2023
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
ME-GY 5443 Make Up Exam 1 Fall 2023
Expectation: 2.5 Hour Exam
Due: Monday at 6:00 pm EST
Problem 1. 25 total points
Below is the magnitude of the steady state response of a SDOF system to some harmonic force, as a function of frequency:
a) Estimate the damping ratio. Use two different methods to calculate ζ .
b) Using one of the values computed for ζ above, estimate the true undamped natural frequency?
c) What is the stiffness and mass of the system if the magnitude F0 of the force input was 100 N in the generation of the plot above?
d) Completely define the free vibration response for this system if: x(0) = 0 anḋ(x)(0) = 100 m/s.
Problem 2. 25 total points
Given a uniform elastic beam of distributed mass per unit length m(̅) , and a rigid body at the tip of mass M and rotary inertia JA at the tip.
The DOF is chosen as the motion of the tip of the beam v(L, t). The length of the beam is L.
Find the equivalent mass meq and equivalent stiffness keq of the SDOF approximation. Follow the technique covered in Lecture 5. Assume small motion theory.
Problem 3. 25 total points
Given the structure below:
a) Derive the differential equation of motion for θ(t).
b) Compute the numerical value of the damping ratio if:
r = 1 (distance shown above, not the frequency ratio)
k1 = 40
k2 = 110
m = 4
c = 0.4
g = 10
c) Completely define the steady state response θ(t) if, in addition to the above:
T(t) = 100 sin(10t) + 40 sin(35t)
2023-12-16