Z transform and its Application on Digital Signal Processing related Questions and Answers

Question :   What is the transient response of the system described by the difference equation y(n)=0.5y(n-1)+x(n) when the input signal is x(n)= 10cos(πn/4)u(n) and the system is initially at rest? 1. (0.5)nu(n) 2. 0.5(6.3)nu(n) 3. 6.3(0.5)n 4. 6.3(0.5)nu(n) Answer :   4 - 6.3(0.5)nu(n)