1. Consider a first-order system with time constant τ and zero initial condition. Find the system’s unit-step response for τ =  and  , plot the two curves versus 0 ≤ ≤ 2 in the same graph, and comment.

2. The temperature of a steel sphere with initial temperature Tsubmerged in water

with temperature Tis governed by the initial-value problem RC +  T  = Ti , T(0) = T0


is the thermal resistance due to convection

is the thermal capacitance of the sphere

Find the temperature of the sphere at any time, as well as its steady-state value.