Q1: If £[f(t)] = F(s), then £[f(t - T)] =

ANS:B - e^-st F(s)

A linear system is one in which the relationship between input and output is linear. All linear system possess the property of superposition i.e., if input u₁ gives output y₁ and input u₂ gives output y₂ then input u₁ + u₂ will give output y₁ + y₂. Superposition implies homogencity i.e., if input u gives output y, then input ku gives output ky where k is a rational number. In general a system is linear if a transformation T satisfies the relation T(au₁ + βu₂) = aT(u₁) + βT(u₂) where a and β are constant.