Question Solved1 Answer rad sec = A second order measurement system has a natural frequency of an = 125 a sensitivity of K = 0.05 [mm], and a damping ratio of 3 = 0.12. If the system is subjected to a step input [F(t) = AU(t)] of A = 75 [mm], determine the 90% rise time and the E5% settling time for a damping ratio of} = 0.15. Plot the response curve and indicate the corresponding rise and settling times.

LYUISH The Asker · Mechanical Engineering

Transcribed Image Text: rad sec = A second order measurement system has a natural frequency of an = 125 a sensitivity of K = 0.05 [mm], and a damping ratio of 3 = 0.12. If the system is subjected to a step input [F(t) = AU(t)] of A = 75 [mm], determine the 90% rise time and the E5% settling time for a damping ratio of} = 0.15. Plot the response curve and indicate the corresponding rise and settling times.
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Transcribed Image Text: rad sec = A second order measurement system has a natural frequency of an = 125 a sensitivity of K = 0.05 [mm], and a damping ratio of 3 = 0.12. If the system is subjected to a step input [F(t) = AU(t)] of A = 75 [mm], determine the 90% rise time and the E5% settling time for a damping ratio of} = 0.15. Plot the response curve and indicate the corresponding rise and settling times.
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Given data:-Natural frequency, omega_(n)=125rad//secSersitivity, k=0.05v//mm{:[F(t)=A uu(t)],[A=75mm]:}{:[" damping ratio "(xi_(1))=0.15],[" Solution:- "T_(lambda)=(pi-theta)/(omega d)],[" where, "quad theta=cos^(-1)xi],[theta=cos^(-1)(0.15)],[theta=81.37]:}converting into radian{:[theta=81.37 xx(pi)/(180)],[theta=0.452 pi],[omega_(d)=omega_(n)sqrt(1-(epsi)^(2))],[omega_(d)=125sqrt(1-(0.15)^(2))],[T_(r)=(pi-0.452 pi)/(123.58)],[T_(r)=(0.548 pi)/(123.58)]:}For, xi=0.12{:[T_(r)=(pi-theta)/(omega d);t ... See the full answer