Derive equation of motion of the following system when the rotation angle theta

Question

Derive equation of motion of the following system when the rotation angle theta is small. The moment of inertia of the uniform rod with mass m about the hinge point is j0 = 1/ 12 ml2. Define the symbols xi, and omega nn in terms of the parameters of the system. Assume that the initial conditions arc theta (0)-theta 0 and theta (0) = omega 0. Obtain the response of the rod. The solution is expressed in terms of the symbols xi and omega n. Write a Matlab program to plot the response. The program takes the parameters k, c, m, and l as well as initial conditions as inputs, and plot the time history of 0(r). Add proper labels to the figure. You must submit your program to me via email. The file name of the file should contain your name and homework-problem number. Assume that mm 1 Okg, and lalm. Use your Matlab program. Plot k vs. c when the damping ratio xi = 1 . Mark the region on the plot where xi > 1 and xi

Explanation / Answer

There are 3 equations of motion

2*a*S=(vf)^2-(vi)^2

vf=vi+a*t

S=vi*t+1/2*a*t^2

the to and fro motion of a body is vibration

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