Question

# 2. the following transfer function governs the rate at which liquid water is boiled off in a boiler, 6 [kg/s], to the pressure of natural gas p [bar] in the supply line that feeds the furnace. G(s):=\frac{B^{*}(s)}{P^{*}(s)}=\frac{200}{3 s+1} an engineer accidentally opened a valve upstream of the process (and quickly closed it after realizing the mistake), causing an under damped oscillation input in the natural gas supply pressure, p*(t) = 1/10 -T sin(2t). \text { write the Laplace transform of the input } P^{*}(s):=\mathcal{L}\left[p^{*}(t)\right] \text {. } \text { write the Laplace transform of the output } B^{*}(s):=\mathcal{L}\left[b^{*}(t)\right] \text {. } ) (2 points) posit a partial fraction expansion of B*(s) in preparation for inverting it to the time domain. (d) (3 points) determine the coefficients in your partial fraction expansion. (e) (3 points) finally, write an expression for the response b*(t) (in the time domain).make sure that your expression is real (i.e. does not contain imaginary numbers).  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7  Fig: 8  Fig: 9