Thank you for your reply, NotSoAccurateNo1.
Angular limits are not relevant to my case because I am not limiting the angle of swinging. I am using linear limit because I wish to simulate the length of the cable by setting the value of linear limit Z. However, that will make the sphere behave strangely.
I modified the sample project to better illustrate the problem. There are now 3 sets of dangling spheres. From left to right:
1: The original swinging sphere
2&3: The spheres are located right below the respective physics constraints so that they will become stable when linear limit (Z) is reached
When play/simulate, a fourth sphere, as it falls, will touch sphere 2 and I expect sphere 2 to just swing left and right slightly. However, it will shake violently like sphere 1.
Link to modified project: 260389-myproject.zip (952 KB)

