Question

Would a basket hanging from 3 equally spaced points above the circumference still swing when forces are applied ( as opposed to bringing the three to one common point of suspension)

Answer 1

I tried to draw what are these two cases:

In case A the basket will not swing as a pendulum with long string. It will swing around that purple point and the period of oscillations will be quite short, because it depends on square root of the length between the point of hanging and the centre of mass:

$$T=k\sqrt{L}.$$

In case A there will be no oscillations between the ceiling and the purple point because that placement of strings creates opposite horizontal forces which prevent the strings from swinging (however, the strings are not hard rods and with big external forces or small circle radius the basket will oscillate):

In case B the basket will swing with longer period, and I think it's better for things inside that basket. Imagine that you are swinging with a period of 1 second or 30 seconds. Big difference. In case B there will be no oscillations between the purple hinge and the basket for the same reason as for A, but the basket will oscillate under the influence of external forces (winds, earthquakes and so on).