The exact solution of a damped Single Degree Of Freedom (SDOF) system is excited by a harmonic force is calculated . It is compared to the numerical solution provided by the Matlab built-in function ode 45, the central difference method, Newmark method and the 4th order Runge-Kutta method, the implementation of which is based on the book from S. Rao .
 Daniel J. Inman, Engineering Vibrations, Pearson Education, 2013
 Singiresu S. Rao, Mechanical Vibrations,Prentice Hall, 2011
E. Cheynet (2020). Harmonic excitation of a SDOF (https://www.mathworks.com/matlabcentral/fileexchange/53854-harmonic-excitation-of-a-sdof), MATLAB Central File Exchange. Retrieved .
Yes, it is possible to do that. However, the central difference is not the best approach. I have uploaded several examples for line-like structures on Matlab FileExchange where the 4th order Runge-Kutta or Newmark mehod is used
is it possible to extend the central difference method to a multiple degree of freedom system?
Hi Vishal Antony,
There won't be much difference in the way to proceed with a rectangular pulse. However, you will probably need a (very) high sampling frequency to properly model the discontinuity that exists in a rectangular pulse.
How to express a rectangular Pulse as forcing function in the numerical method e.g. central difference method?
@Maede I agree with you. I have re-arranged the inputs of the function "Newmark" in the new submission
I think it would be nicer if you had the inputs for both functions (CentDiff and Newmark) in the same order. Just to look better, no big deal :)
Added project website
The inputs of the Newmark-Beta funciton are ordered to be consistent with the function CentDiff
Added Newmark and Runge-Kutta methods
- picture added