A measurement system can be modeled by the equation given below \frac{7}{8}\dot{y}+y=F(t) The...


A measurement system can be modeled by the equation given below

{eq}\frac{7}{8}\dot{y}+y=F(t) {/eq}

The output signal is initially steady at 2 V. The input signal is then suddenly increased to 8 V.

i) Determine the response of the measurement system.

ii) Plot both input signal and the system response from t = 0 s through the steady response. Provide proper legend so as to identify the signals.

Response Measurement Of System:

To determine the response of a system we solve the given input signal function and find the solution of the differential equation.We thus substitute the value of the initial conditions for the signal to get the output of the signal.

Answer and Explanation: 1

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(i) {eq}F(t)=\left\{\begin{matrix} 0 , t\leq 0\\ 8,t>0 \end{matrix}\right. {/eq}

For t<0,y=2

{eq}\frac{7}{8}\dot{y}+y=F(t)\\ y(t)=ce^{-t/...

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