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.