Question Solved1 Answer PLEASE EXPLAIN EVERY STEP CLEARLY. THANK YOU 3.21 Determine the frequency bandwidth in hertz, the low cutoff frequency, and the high cutoff frequency of a first-order thermal sensor having a time constant of 0.10 s when subjected to the sinusoidal temperature variation, T(t) = 20 sin otºC.

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Transcribed Image Text: 3.21 Determine the frequency bandwidth in hertz, the low cutoff frequency, and the high cutoff frequency of a first-order thermal sensor having a time constant of 0.10 s when subjected to the sinusoidal temperature variation, T(t) = 20 sin otºC.
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Transcribed Image Text: 3.21 Determine the frequency bandwidth in hertz, the low cutoff frequency, and the high cutoff frequency of a first-order thermal sensor having a time constant of 0.10 s when subjected to the sinusoidal temperature variation, T(t) = 20 sin otºC.
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Solution: By using First order differential equation we cun modeled Muny mechanicul, electricul and thermul systems.rarr An one degree of Freedom First order system is governed by the First order ordinary differentiul Equations:{:[91(dy(t))/(dt)+90 y(t)=F(t)-(1)],[" Where, "y(t)=" temperature, "],[F(t)=" Forcing Function, "T(t)]:}Therefore, (tau dy(t))/(dt)+y(t)=kT(t)-(2)" Where, "{:[k=1//u_(0)=" guin of system "],[tau=41//40=" Time constant "(tau=0.1s)]:}Applying Lupluce transform on both sides of equations,{:[y(s)[tau s+1]=K_(0)T(s)],[(y(s))/(T(s))=(K_(0))/(tau s+1)=H(s)" is the transfer Function "],[" in lupluce domain "],[H(j omega)=(k_(0))/(jw tau+1)(s rarr j omega)]:}Mugn ... See the full answer