Question

1. Note: Drawings are not to scale.) You are given two objects, each with the same mass. One object is a solid, uniform disk of outer radius R The other object is a thin, uniform rod of unknown length Initially these objects are suspended as shown (each from a frictionless pin located on its uppermost edge). When allowed to oscillate freely as pendulums (through small angular displacements), they have equal frequencies. disk rod Then the rod is removed from its pin and attached instead to the end of a massless ideal spring suspended from the ceiling, with a y-axis defined as positive downward (and y =0 at the ceiling), as shown. You may ignore all friction, air drag and spring fatigue The rod-spring system is set into vertical oscillation so that all of the following are true * The position of the rod's upper end is given by y(,)-Acos(or + + H, where , is in seconds The spring is compressed for some time interval during each cycle of oscillation At a certain position in each cycle, the rod experiences a maximum net force magnitude F and-letting Ua for the system be defined as zero at that same position- the total mechanical energy of the system is a constant known value,E 0.123 s, the lower end of the rod reaches its greatest distance. D. from the ceiling for the firsttime . At The known data: D 0.987 m g = 9.30 m/s: R 0.124 m H 0536 m F-tau = 34.2 N Emwh = 1.60 J a. Find the relaxed length of the spring. b. Find the arm length of a simple pendulum whose period is three times the period of the rod-and-spring system c. Find the y-velocity (both magnitude and direction) of the rod at time 1 = 4.65 s.

Answer 1

attoled t octUak a ung, tree, hade- tancles der The mantmm

gita z8m - at t-o . 3.

Or tho od -Vesco-