Name ___________________________ EM406 Examination II October 30, 2008 Problem Score 1 /30 2 /40 3 /30 Total /100 Show all work for credit AND Stay in your seat until the end of class AND Turn in your signed help sheet NOTE: Don’t get bogged down on short answer problems! You should only spend about 15 minutes on these problems!Name 30 pts EM406 Examination III Problem 1 October 30, 2008 Problem 1.1 A lightly damped SDOF linear dynamic system that has the following transfer function9009002sss is forced with a periodic function shown below (this is a base motion problem). What do you need to input into your Maple Worksheet to solve this problem? (3 pts) Using your Maple Worksheet, write down the first three non-zero terms in the Fourier series and in the steady state solution (only keep 3 decimal places to save time). (6 pts) F(t) = ___________________+____________________+__________________________ x(t) = ___________________+____________________+__________________________ About how many terms do you need to keep? (2 pts) y(t) (mm) time 2 4 1 – 0.5 tProblem 1.2 What is the difference between a shaker test and a roving hammer impact test from a theoretical standpoint and a realistic/practical standpoint? (4 pts) Theoretical: Realistic/practical: Problem 1.3 (3 pts) Why would you have to add a small amount of damping in a Simulink model of the system shown below in order for the Simulink out to match the theoretical steady state response? txxsin50700700700110020010 Problem 1.4 What is the difference between the peak-pick method and the one that used fminsearch? (5 pts)Problem 1.5 The magnitude and phase of a primary system which has had a vibration absorber atttached to it is shown below. Knowing the mass of the absorber is 1 kg, what is the stiffness of the absorber spring? (4 pts) Problem 1.6 If the system described the FRF’s shown in Problem 1.4 were forced with f(t) = 5cos15t N determine the steady-state response of the primary mass. Note that you do not need to be able to do Problem 1.4 to do this problem. (3 pts) 0 5 10 15 2010-410-310-210-1Frequency (rad/s)Magnitude of FRF (m/N)0 5 10 15 20-200-150-100-50050Frequency (rad/s)Angle of TF (degrees)Name 40 pts EM406 Examination III Problem 2 October 30, 2008 You find that a system has the equations of motion (with numbers): 0013002002008001500100GGxx Determine: a) The natural frequencies and modes for this system. You may use Maple or Matlab or solve by hand. If you use Maple or Matlab show enough work so I know you could do it by hand if necessary. b) Accurately sketch the mode shapes, labeling the relative displacement of the center of gravity and the displacement of the right end of the bar assuming L2 = 1.5 m. c) A motor of mass of 20 kg and an unbalance of 0.02 kg-m is placed at the center of gravity determine the steady-state response for xG and  assuming  = 9 rad/s. Save the numerical solution to the end – if you have a set of algebraic equations and a list of unknowns that is sufficient for most the points. xG G L1 L2 k1 k2 Name 30 pts EM406 Examination III Problem 3 October 30, 2008 Two mass are attached to the end of light rods that are connected by a spring as shown below. The system is forced harmonically with the force f(t) = Fsint. a) Using Lagrange’s equations determine the equations of motion for the bar and block. For your final answer, assume small angles. No credit will be given if you do not use Lagrange’s equations. O a L1 m1 F1(t) = F0sint k1 O a m2 L2