1. Given a system with the transfer function Y(s)/X(s) = (Tls + l)/(Tzs + 1). Find Y(r) if X(t) is a

1. Given a system with the transfer
function Y(s)/X(s) = (Tls + l)/(Tzs + 1). Find Y(r) if X(t) is a unit-step
function. If Tl/T2 = 5, sketch Y(r) versus tlT2. Show the
numerical values of minimum, maximum, and ultimate values that may occur during
the transient. Check these using the initial-value and final-value theorems of Chap.
4.

2. A thermometer having first-order
dynamics with a time constant of 1 min is placed in a temperature bath at
100F. After the thermometer reaches steady state, it is suddenly placed in a
bath at 110F at t = 0 and left there for 1 min, after
which it

1. Given a system with the transfer
function Y(s)/X(s) = (Tls + l)/(Tzs + 1). Find Y(r) if X(t) is a unit-step
function. If Tl/T2 = 5, sketch Y(r) versus tlT2. Show the
numerical values of minimum, maximum, and ultimate values that may occur during
the transient. Check these using the initial-value and final-value theorems of Chap.
4.

2. A thermometer having first-order
dynamics with a time constant of 1 min is placed in a temperature bath at
100F. After the thermometer reaches steady state, it is suddenly placed in a
bath at 110F at t = 0 and left there for 1 min, after
which it is immediately returned to the bath at 100F.

(a) Draw a sketch showing the variation
of the thermometer reading with time.

(b) Calculate the thermometer reading at
t
=
0.5 min and at t = 2.0 min.

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