Dynamics 13.013 , Problem Set 10, Due November 29, 2000
1a & 1b. Do problem 8.12 in the text. Include a damper and use the parameter values
given below in obtaining a solution. vo= 340 m/s, k = 5000 N/m, m = 0.01 kg, and M=4 kg.
1c. The damper results in damping which is 5% of critical. What is the value of the
dashpot constant R. In solving for the motion, put your answer in the form
x(t)=Acos(wt - phi)e^-zeta*wn*t.
1d. Sketch the motion as a function of time.
2. Do problem 8.6 parts a, b, and c. Also add a part d as given below.
Let r = 3R/4, R = 0.2m, M = 2.0 kg, k/m = 5 N/m-kg
d. Connect a dashpot in parallel to the spring. Assume the dashpot connects to the
rotor at R/2 on the same radius line as the spring. Find the dashpot constant which
will result in 10% of critical damping.
3. Consider problem 6.92. Find and expression for the equation of motion
and find an expression for the undamped natural frequency.
4. Do 8.13.
5. Conduct an experiment on a single degree of freedom oscillator. Estimate the natural
frequency and damping ratio for your system. Report in orally on Monday on the
experiment if you have not done so already. Turn in a brief writeup with the homework.
It has to be good enough that I could reproduce it.