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  3. problem 4 the imperial fleet discovered the rebellion base in...

Question: problem 4 the imperial fleet discovered the rebellion base in...

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Problem 4. The imperial fleet discovered the rebellion base in the Hoth system, and de- ployed the giant AT-AT Walkers (figure(a)) on the surface to find and destroy the rebelion shield generators. They were able to destroy their target but not before Luke Skywalker and other rebels could flee from the planet. Many of the storm troopers blamed this on the poor performance of the Walkers. In particular, they reported that the vibration in the cockpit was too annoying, and the primary inspection showed that the dampers in the robot legs are not sufficiently damping the vibrations. The empire has hired you to find the problem and fix it (They are evil but they pay handsomely!) Figure (b) shows your vibration model for the Walker: The body weighs 50 (metric) tons and it is sitting on 4 titanium legs. Each leg is acting as a spring fixed to the ground, with a stiffness of 5 × 1010N/m. The legs are equipped with identical dampers of unknown damping coefficient. The mass moves up and down without any tilting or rotational motion (implying that the displacement of springs are equal) 1. By doing some tests on one of the Walkers, you find out that the peak-to-peak oscil- lation decays by 9.5 percent in each cycle. Compute the unknown damping coeffi cient of each leg. (Hint: use logarithmic decrement.) 2. The design protocol for vehicular robots in the Galaxy says that the minimum peak- to-peak decay required for human operation is 22 percent. Find the range of values for the damping coefficient of each damper that satisfies this requirement Report the correct answer to the empire or you will meet your destiny at the hands of Lord Vader!

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