Homework 2 ME5305 Due Sept 7

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me 5305
  Homework 2 ME/AE 5305 Due Sept. 7, 2017 Emmadi, Vamshi 1000804218 Consider the differential equation below for y(t) with input u(t). 3⃛+75̈ + 1800̇ + 7500 = 600̇ + 15000  (a) Is the differential equation linear or nonlinear? The above Differential Equation is linear  since it satisfies the linearity conditions. A differential equation is linear if the dependent variable and all its derivative occur linearly in the equation i.e., there are no products of the function of ‘y’ and its derivatives and neither the function or its derivatives occur to any power other than the first power. (b) What is the order of the differential equation? The differential equation is 3rd  order differential equation (c) What is the transfer function for y? (d) What is the DC gain of this transfer function?  (d) Enter the transfer function into MATLAB using the ‘tf’ command and use the ‘damp’ command to get the eigenvalues. (e) What are the time constants? ____________ (f) What is the time required for the solution of this differential equation to reach steady state within 1%? ________ (g) What is the damping ratio? _____ (h) What is the undamped natural frequency? _____  (i)   What is the damped natural frequency? _____ (j) Assume that the input u(t) is a constant of 10; y(t) will also become a constant with what value? ________ (k) If the initial value of y(t) is 15 at t = 0, estimate the plot of y(t) starting at t = 0 out to the approximate final time associated with reaching steady state (when y becomes a constant). y(t)0time, t s  
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