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  3. consider the springdamper system shown in figure 1 fa figure...

Question: consider the springdamper system shown in figure 1 fa figure...

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Consider the spring-damper system shown in Figure 1. fa) 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(t) (3)Write the solution x(t) as the sum x(t)- x (t)+x, (t) and do the following: a) give the name of x(t) b) write the equation that x (t) 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 x, (t) and give its name e) Graduate Work: can one write a general expression for x, (t)? If not, then why not? (4)Discuss the meaning offree response and forced response (5)Numerical work: for k = 180 N/m, c = 270 N/(m/s), use MATLAB to do the following a) display input data b) calculate the time constant T; give the numerical value and units

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