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 ≤ t ≤ 2 in the same graph, and comment.
2. The temperature of a steel sphere with initial temperature T0 submerged in water
with temperature Ti is governed by the initial-value problem RC + T = Ti , T(0) = T0
R is the thermal resistance due to convection
C is the thermal capacitance of the sphere
Find the temperature of the sphere at any time, as well as its steady-state value.