I am doing some study into longitudinal wave dynamics. I am using theoretical models of wave motion in continuous bar and comparing this to numerical analysis using a lumped mass model. So far I have discovered that the continuous bar vibrations, caused by base support motion (i.e. vibration caused by the entire bar moving) excites and infinite number of natural modes (with the lower ones having a higher contribution). When modelling this with mass-spring-mass-spring...etc. of the same length and wave speed (i.e. a=sqrt(E/ro) ) only the first natural mode seems to be excited. Am I modelling my numerical system wrong, or can it only capture the first mode?