Question Solved1 Answer 3.4 A measurement system can be modeled by the equation 0.5y + y = F(t) Initially, the output signal is steady at 75 volts. The input signal is then suddenly increased to 100 volts. a. Determine the response equation. b. On the same graph, plot both the input signal and the system time response from t=0 s through steady response.

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Transcribed Image Text: 3.4 A measurement system can be modeled by the equation 0.5y + y = F(t) Initially, the output signal is steady at 75 volts. The input signal is then suddenly increased to 100 volts. a. Determine the response equation. b. On the same graph, plot both the input signal and the system time response from t=0 s through steady response.
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Transcribed Image Text: 3.4 A measurement system can be modeled by the equation 0.5y + y = F(t) Initially, the output signal is steady at 75 volts. The input signal is then suddenly increased to 100 volts. a. Determine the response equation. b. On the same graph, plot both the input signal and the system time response from t=0 s through steady response.
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  Sol ^(n)(a) The given equation{:[f(t)=0.5(dy)/(dt)ty],[0.5(dy)/(dt)+y=100]:}Take Laplace transfam{:[0.5(sy(s)-y(0))+y(5)=(100)/(5)],[0.5(SY(s)-75)+Y(s)=(100 )/(s)],[y(s)(0.5 s+1)-0.5 xx75=(100 )/(s)],[y(s)=>(((100 )/(s)+(75)/(2)))/(0.55+1)],[y(s)=>(200+75 s)/((2s)xx(0.55+1))],[y(s)=(2.00+75 s)/(s(s+2))] ... See the full answer