1. A big slug weighing 10 pounds stretches a spring 4 foot. The slug is removed and replaced by a smaller slug, of mass 1.6 slugs. The slug on the spring is then placed in an environment that produces a damping force that is approximately equal to 2 times the instantaneous velocity and then released from a position 1/3 foot above equilibrium with an downward velocity of 5/4 feet per second. (a) Clearly identify m, ß and k and use these constants to set up the DE for this situation and show all the steps to find the position equation for the spring. Use X for the position and t for the time. Round all coefficients to 2 decimal places. (b) Graph X(t), labeling the axes and use your graph to find the first time where the slug passes equillibrium, heading upwards. Label this point on your graph and write a sentence to summarize your findings...as always.

1. A big slug weighing 10 pounds stretches a spring 4 foot. The slug is removed and replaced by a smaller slug, of mass 1.6 slugs. The slug on the spring is then placed in an environment that produces a damping force that is approximately equal to 2 times the instantaneous velocity and then released from a position 1/3 foot above equilibrium with an downward velocity of 5/4 feet per second. (a) Clearly identify m, ß and k and use these constants to set up the DE for this situation and show all the steps to find the position equation for the spring. Use X for the position and t for the time. Round all coefficients to 2 decimal places. (b) Graph X(t), labeling the axes and use your graph to find the first time where the slug passes equillibrium, heading upwards. Label this point on your graph and write a sentence to summarize your findings...as always.