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A mass on or attached to a spring enters resonance upon being excited. Unlike a pendulum, its frequency does not depend on gravity. See http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html
The accompanying program provides a simulation of such a resonance. The program is suitable for iPad and iPhone. The following screenshots show, successively, the normal view on an iPad and, next to it, the view during the simulation of an iPhone.
The iPhone simulation can optionally be activated by setting iPhoneTest=1 in the Presets.
Another option in the Presets is 'DoubleQuit'. If this is set to 1, the 'Quit' button will need to be pressed twice to end the program. In the meantime, you have the option to take a screenshot.

Nice graphics!
It would be really interesting to have a simulation of a system with two balls and two springs, the second spring “piggybacked* to the other.
If the spring constants and the ball masses could be set by sliders, interesting ball movements could be investigated.
The math of the two ball system is far more difficult, but it is not needed as the simulation uses very small time steps.
One can simply apply Newtons law F=m.a (or a=F/m) in this case) twice in each time step.

That is too difficult for me

Sounds like a challenge. I may attempt it.

I did write a program of 1 or 2 satellites orbiting the earth using the same principle of small increments. It only uses the well known gravitational equations like F=g*M1*M2/d^2 and a=F/M to calculate a new position of the satellites at each moment in time with chosen starting parameters. I'll let you know if I do. For some reason I enjoy writing simulation programs.

davey110 wrote: ↑

Fri Aug 28, 2026 4:17 am

Sounds like a challenge. I may attempt it.
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I am very interested in your approach and the result.