On Beck's problem

Instability of a Quasi-Dynamic System Subjected to a Circulatory Force

“…G=<i=K2 =°t the effect of weight 1s Ignored and the two horizontal springs are absent; (b) K..=K2 = 0, the effect of weight is retained but the horizontal springs are absent; (c) G = K-I=0, the spring at B In Figure 1 is included in the system but the effect of weight 1s ignored and the spring at A 1s absent; (d) G=K =0, the spring at A 1s present in the system, whereas the effect of weight is Ignored and the spring at B is absent.so that (10) can be expressed as w 2 = CO-cOQ2 -3(l-a)Q+l]/y 2 (5-2Q) a, these elgencurves reveal the possibility of multiple Intervals of stability and instability relative to the load parameter Q. The case of a=l/5 1s exceptional, however, because (17) assumes the rather simple form u>?…”