Question Solved1 Answer A measuring system has a natural frequency of 0.5 rad/s, a damping ratio of 0.5, and a static sensitivity of 0.5 m/. Find y(t) and estimate its 90% rise time and settling time if F(t) = 2 U(t) and the initial condition is zero.

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Transcribed Image Text: A measuring system has a natural frequency of 0.5 rad/s, a damping ratio of 0.5, and a static sensitivity of 0.5 m/. Find y(t) and estimate its 90% rise time and settling time if F(t) = 2 U(t) and the initial condition is zero.
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Transcribed Image Text: A measuring system has a natural frequency of 0.5 rad/s, a damping ratio of 0.5, and a static sensitivity of 0.5 m/. Find y(t) and estimate its 90% rise time and settling time if F(t) = 2 U(t) and the initial condition is zero.
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Given:- Natieal frequency omega_(n)=0.5rad//s Damping retio epsi=0.5Soln:-{:[(" Output "(s))/(" Input "(s))=f(s)=(0.5 xxomega_(n)^(2))/(s^(2)+2epsiomega_(n)s+omega_(n)^(2))],[=(0.5 xx(0.5)^(2))/(s^(2)+2xx0.5 xx0.5 s+(0.5)^(2))],[=(0.125)/(s^(2)+0.5 s+0.25)]:}For steady state value put s=0 in F_(f) so steady state value =0.5f(s)=(0.125)/(s^(2)+0.55+0.25)Poles at s=-0.25+-j 0.433So, y(t)=A+ ... See the full answer