1. Engineering
  2. Mechanical Engineering
  3. consider the massspringdamper system shown in figure 2 figure 2...

Question: consider the massspringdamper system shown in figure 2 figure 2...

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Consider the mass-spring-damper system shown in Figure 2 Figure 2: spring-damper system (1)Draw FBD and deduce EOM. Clearly state your assumptions (2)Extract the homogenous equation from EOM and process it a) Assume x(t) Cand deduce the characteristic equation b) Solve the characteristic equation and find p12 in terms of m,c,k c) Define critical damping cr and damping ratio in terms of m,c,k d) Recall the natural frequency ωη in terms of m, k e) Write p1,2 in terms of ahς f) Write damped vibration frequency o in tems of natural frequency ø and damping ratio Write the complementary solution, xc(t) in terms of ωπζ and some constants C, φ the relation between f(t) and f(t) and a particular solution xt) can one write a general expression for X, (t)? If not, then why g) (3)Cast EOM as an ODE in standard form in terms of and the forcing function f(t). Write (4)Graduate Work: Write the general solution x(t) in terms of complementary solution x (t) not? (5) Numerical work: for m-8 kg, c 10N/(m/s), k- 600 N/m, use MATLAB to a) display input data b) calculate the natural frequency a, damping ratio , damped vibration frequency a: give the numerical value with appropriate units

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