chbe2120fall2010hw4

# chbe2120fall2010hw4 - ChBE 2120 Homework 4 Due Friday...

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ChBE 2120, Homework 4 Due: Friday, September 17, at 8:05 am Consider the problem in Chapra and Canale, 25.16: The motion of a damped spring-mass system is described by the following ordinary differential equation: 0 2 2 = + + kx dt dx c dt x d m Where x = displacement from equilibrium position (in meters), t = time (in seconds), m = 20 kg, c = the damping coefficient (in N*s/m). Assume the damping coefficient takes on the value of 5, an underdamped system. The spring constant k = 20 N/m. The initial velocity is zero, and the initial displacement x = 1 m. Solve this equation over the time period 0 t 15 s. Develop a MATLAB code that integrates this system of differential equations using Euler’s method. Do the following steps: (1) First, convert this equation to a system of differential equations that can be solved using the methods we have learned and using MATLAB. (2) Write a function that contains this system of differential equations. It should take two inputs: the time and a column vector of two elements containing the two variables for which you should be solving, which I will arbitrarily call y 1 and y 2 . It should return a column vector containing the time-derivatives of y 1 and y 2 . Name this function springDerHw4_myGtAccountId.m.

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