67 o In Fig. 15-51, three 10 000 kg ore cars are held at rest on a mine railway using a cable that is parallel to the rails, which are inclined at an- gle e = 30°. The cable stretches 15 breaks free cm just before the coupling between the two lower cars breaks, detaching the lowest car. Assuming that the ca- ble obeys Hooke's law, find the (a) frequency and (b) amplitude of the resulting oscillations of the remain- ing two cars. Car that Figure 15-51 Problem 67.

IC-3 A 167 gram mass is vibrating about its equilibrium position on the end of a spring as shown in problem SHM-8. While vibrating, the mass is observed to have a maximum speed of 0.500m/s and a maximum acceleration of 6.00m/s. At t0 the mass is at the equilibrium position with a velocity to the left. a) Find the numerical values for the angular frequency o and the amplitude of the motion xm. Hint: think about how Vm and xm are related. b) Find the value of the spring constant of the spring. c) The position of the block is described by x Xmcos(@t+0,). Find all possible values of 0, and then explain how to determine the value of 0, that corresponds to the given conditions. 99+ hp

A 64 lb weight is attached to the lower end of a coil spring suspended from the ceiling, the spring constant being 18 lb/ft. The weight comes to rest in its equilibrium position. It in then pulled down 6 inches below its equilibrium position and released at t = 0. At this instant, an external force given by F(t) = 3 cos wt is applied to the system. (i) Assuming the damping force in pounds is numerically equal to 4(dx/dt), where dx/dt is the instantaneouse velocity in feet per second, find the displacement as a function of the time and determine the resonance frequency of resulting motion. (ii) (ii) Assuming there is no damping, determine the value of w which gives rise to undamped resonance.

Help me for part (A) only,To find the torsional constant expression.