Difference in Simulation Mass Damper System

I'm not familiar with 20 SIM. Can you give a comparison of the results? How different are the differences?

In my experience with simulating mass/spring/damper systems, sample time (step size, delta time) plays a critical role in the accuracy of the simulation. The same goes for the type of digital integrator that's used (Euler, Rectangular, Trapezoidal, Runge-Kutta).

This can be because of almost anything. You may have a typographic error in your numeric entries (both hand and program) to using simpler equations in the hand calculation that ignore a nuance.

The real question is which method agrees with measured responses with reality?

Hard to say, perhaps this will help....

https://www.youtube.com/watch?v=WVzhShQG40M

http://academic.amc.edu.au/~hnguyen/JEE326IPC/Simulink_Tute_04.pdf

http://www.20sim.com/downloads/files/20simGettingStarted43.pdf

While I'm not familiar with the "20 sim", your mention of "hand calculations" leads me to conclude that while the data might be identical for both methods, the sim calculates the results to a more precise value than the hand-e.g. 23 places versus 10 or 12 by hand.