Problem

In this problem we will explore an assumption that we have made, namely, that we can negle...

In this problem we will explore an assumption that we have made, namely, that we can neglect the mass of cables or ropes in pulley systems.

Consider the simple pendulum in the left part of the figure. Let the pendulum bob be set in motion in the position shown with a speed υ0 = 3 m/s. Determine the motion of the pendulum bob and, in particular, its maximum displacement from its starting position. Next consider a double pendulum with an equally long cord but with a cord of mass mC. In order to gain an appreciation for the effect of the mass of the cord on the pendulum’s motion, let the entire mass of the cord be lumped at its midpoint (we then neglect the mass of the two cords connecting O to mC and mC to mB). Next let this double pendulum be set in motion in the same way as in the previous case. Again, determine the motion of the pendulum bob mB, and determine the value of mC necessary to cause a 10% difference in the maximum displacement from its starting position.