**MECH 351 – MODELING AND ANALYSIS of DYNAMIC SYSTEMS II**

**Please complete your work NEATLY on SEPARATE paper. Do not submit your work on this handout.**

- (20 points) Determine the solution for with and and write the closed form expression of the response.

2 (40 points) A tuning fork is being evaluated with how it is damped by fluids with different viscosities. The damping ratios for these test fluids are . Plot for this system assuming a natural frequency of with the initial conditions of: . Attach a hard copy of your code (or your Excel file) to your HW submission. Your figure should include a legend and should be easy to discern one curve from the other (i.e., line specifiers – MECH 102, say what??? – you can also do this in Excel)

- (20 points) Consider the below system where a simple pendulum is connected to a spring. You can assume that the mass of the pendulum rod is negligible. Using the methods discussed in this lesson, derive the equation of motion for this system. Once completed, linearize the system for small angles and determine the natural frequency. The length of the pendulum is
*l*, the mass is*m,*and the spring stiffness is*k.*