Question

A. 1st Order Systems Consider the spring-damper system shown in Figure 1. Figure 1: spring-damper system (1)Draw FBD and deduce EOM. Clearly state your assumptions. (2)Cast EOM as an ODE in standard form; write the time constant T and the forcing function f(t) in terms of k,c, f*(1) (3) Write the solution x(t) as the sum x(t) = x (1)+x,() and do the following: a) give the name of x (1) b) write the equation that x(!) must satisfy and give its name c) write the general expression of x (t) in terms of T and an unknown constant C d) explain the role of xy(t) and give its name e) Graduate Work: can one write a general expression for x,(e)? If not, then why not? (4) Discuss the meaning of "free response" and "forced response" 2 (5)Numerical work: for k=300 N/m, c = 500 N/(m/sec), use MATLAB to do the following: a) display input data b) calculate the time constant T; give the numerical value and units

Answer 1

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