Name ___________________________ Section _____________________ EM406 Examination I September 30, 2008 Problem Score 1 /10 2 /30 3 /30 4 /30 Total /100 Show all work for credit AND Turn in your signed help sheet AND Stay in your seat until the end of className 10 pts EM406 Examination I Problem 1 September 30, 2008 Problem 1c (3 pts) Assuming you designed an isolator (assuming zero damping and a reduction of force of 80%) will the actual reduction be larger or smaller since the real system will have some damping? Problem 1d (3 pts) A mass M is connected to a non-linear spring that has the force deflection curve shown. Would you expect the spring-mass system to have a larger frequency in configuration 1 or configuration 2? (circle one and briefly explain why) Problem 1e (4 pts) A system with an unbalance of 0.1 kg-m has the magnitude frequency response plot shown below. What is the mass of the system? 0.1 0.2 0.3 x (inches) 1 3 5 F (lbf) Non-linear spring M Configuration 2 SEP z Non-linear spring M Configuration 1 0246810120 1 2 3 4 5 6Frequency ratioMagnitude (mm)Name 30 pts EM406 Examination I Problem 2 September 30, 2008 An electric motor weighs 500 lb and runs at 1800 rpm (188.5 rad/s). The rotor has a weight of 100 lb with its mass center located at a distance 0.01 in. from the axis of rotation. Determine a) The force transmitted to the ground if the motor were rigidly bolted to the ground. b) The force transmitted to the ground if the motor is supported on four steel helical springs (E = 30x106 lb/in2, G = 11.2x 106 lb/in2), each of which has eight active coils with a wire diameter of 0.5 in and a coil diameter of 3 in. (Save all the numerical calculations until the end – just show me the equations you would use and the numbers you would plug in. If you have time at the end then go ahead and do the calculation).Name 30 pts EM406 Examination I Problem 3 September 30, 2008 A unicyclist decides to tryout a new invention that is supposed to help novice riders. The invention consists of a helmet that is connected to a horizontal track by a spring as shown below. Assume the road is sinusoidal with 1.5 m between peaks and 0.1 m from peak to trough and his speed v is known. Determine a) The equation of motion (this means show all work) b) The steady state amplitude for the mass m. k1 c k2 m v x SEPName 30 pts EM406 Examination I Problem 4 September 30, 2008 A uniform slender rod of known mass m and length L is pinned at point O. If the system is displaced and released from rest the resulting oscillation decays by 20% after 3 cycles and has a frequency of 10 rad/s. a) Determine the equations necessary to determine k and c. DO NOT SOLVE. I want is a set of equations and a list of unknowns. b) How would your answer change if the spring were not ideal, but had a mass mspring? k O c m, IG = 1/12 mL2 L L/4 G