219 hw2 and solution from 2005

Elementary Differential Equations, with ODE Architect CD

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Math 219, Homework 2 Due date: 23.11.2005, Wednesday This homework concerns two (fictitious) design problems about the solar car “MES ¸- e” of the METU Robotics Society, which won the Formula-G trophy in September 2005. Just for the purposes of this homework, assume that they want to modify the car, and they are asking for your help on two issues. 1. The first problem is about the shock absorbing system of the car. We may model the shock absorber as a single linear spring. This question concerns how to adjust the damping coefficient in order to meet certain requirements. (a) It is known that when the pilot, weighing 80 kg , gets into the car seat, the shock absorber is compressed by 5 cm . From this data, compute the spring constant k (in kg/sec 2 ). (b) The car (without the pilot) weighs 240 kg . Write a differential equation which governs the vertical motion of the car (this could for instance describe the vertical
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displacement when the car goes over a speed bump). (Hint: Check “Damped free vibrations” from Boyce,Di Prima, section 3.8).
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