Can I calculate a sinus function that has kind of elbows / round steps in it ? Or if I could get hold on the second curve. I need one of these functions for some graphical design. How would the formula for the periodic curve look like ? Can I use it with simple mathematics ?
(It will be applied to a computer program. So it might contain a few steps and provisional results)
1)

Sorry, both drawn in Paint XP.
2)

Your first graph looks rather like $\sin(x) - \sin(x)^3/3$.