I want to calculate the random response of a MDOF system (Response of the system when it is being excited at some of its DOFS by a zero-mean random excitation). The system is a simple 5 DOF lumped mass-spring system. I derived the mass, damping, and stiffness matrices of the system. Next, I rewrote the governing differential equation of the system (Mx'' + Cx' + kx = f) in the from q' = f(q) in order to use ode45 to calculate the time domain response of the system. The code works well when the system is excited by lets say sin(2*pi*f*t) or step function or... . However, when I use a random number generator rand or randn to excite the system with a zero-mean random process, it takes the code too much to reach the answer. The time is too long (due to too short time intervals of the solution process in ode45). Can anybody say if there is another way to calculate the random response of an M,C,K model?