Resilience in a Mechanical System a mass m is attached to one end of a massless spring with a force constant k and an unscratched length 10 the other end of the spring is free to turn about a nail driven into a frictionless, horizontal surface (Fig. 13.44). The mass is made to revolve in a circle with an angular frequency of revolution.
(a) Calculate the length 1 of the spring as a function of cu.
(b) What happens to the result in part (a) when approbation the natural frequency cu = Wm of the mass-spring system? (If your result bothers you, remember that massless springs and frictionless surfaces don’t exist as such, but are only approximate descriptions of real springs and surfaces. Also, Hooke’s law is only an application of the way real springs behave; the greater the elongation of the spring, the greater the deviation from Hooke’s law.)