Consider a critically damped mass-spring-damper system with a response x(t) = (C+Ct)e-wnt such that r(t) =...

   

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Consider a critically damped mass-spring-damper system with a response x(t) = (C₁+C₂t)e-wnt such that r(t) = [xo + (vo + xown)t] ewnt as graphically shown below with accompanying tab- ular data. displacement r(t)/[m] 1.1 1.2 1.3 0.06 0.05 0.04 0.03- 0.02 0.0 t/[s] 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.1 time t/[s] 0.2 displacement. x(t)/[m] t/[s] x(t)/[m] 0.04500000 0.16 0.03741301 0.05486737 0.18 0.03269398 0.05873785 0.20 0.02832805 0.05866778 0.22 0.02437076 0.05612005 0.24 0.02083955 0.05212137 0.26 0.01772728 0.04737986 0.28 0.01501155 0.04237310 0.30 0.01266133 -1 The above system is known to have a spring of spring constant k = 2356 N m however no further information is known apart from the rough estimate that 10 wn/[rad s-¹] < 15. Considering the above system, using any appropriate mixture or combination of analyti- cal equations and/or graphical methods and/or numerical methods, determine the following information: 0.3 The natural angular frequency wn and initial velocity *o; The damping constant c; The velocity v(t) = x(t) evaluated at time t = 0.35 s; (10) (5 Consider a critically damped mass-spring-damper system with a response x(t) = (C₁+C₂t)e-wnt such that r(t) = [xo + (vo + xown)t] ewnt as graphically shown below with accompanying tab- ular data. displacement r(t)/[m] 1.1 1.2 1.3 0.06 0.05 0.04 0.03- 0.02 0.0 t/[s] 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.1 time t/[s] 0.2 displacement. x(t)/[m] t/[s] x(t)/[m] 0.04500000 0.16 0.03741301 0.05486737 0.18 0.03269398 0.05873785 0.20 0.02832805 0.05866778 0.22 0.02437076 0.05612005 0.24 0.02083955 0.05212137 0.26 0.01772728 0.04737986 0.28 0.01501155 0.04237310 0.30 0.01266133 -1 The above system is known to have a spring of spring constant k = 2356 N m however no further information is known apart from the rough estimate that 10 wn/[rad s-¹] < 15. Considering the above system, using any appropriate mixture or combination of analyti- cal equations and/or graphical methods and/or numerical methods, determine the following information: 0.3 The natural angular frequency wn and initial velocity *o; The damping constant c; The velocity v(t) = x(t) evaluated at time t = 0.35 s; (10) (5