Unit Step Function
Unit Step Function : A unit step function is a function which has a zero value for t≤t₀ and then rises instantaneously to a sustained unity value. This is shown in the figure below. In electric circuit , and in mechanical system it could represent a force suddenly impressed on the system . This unit step function starting at zero time will be designated by u(t) , and that starting at time t₀ is u(t-t₀) . Thus { 0 for 0<t≤t₀ u(t-t₀) ={ { 1 for t>t₀ .....(1) The Laplace transform of unit step function is ...