The student who manages to correctly determine S to the most decimal places gains an extra ten points on the problem set. This problem may sound like it is full of arbitrary functions, but there is a physical content to these manipulations that will become clearer later in the course. For the moment, we can just look on them as exercises in numerical equation solving. Here, t is an adjustable parameter, and we want to find all values of u which make the equation true for a given t . That is, the body is connected by a spring to the origin, and experiences a drag-froce proportional to its velocity.
Lets assume that all motion is along the x-axis.
There are two possible solutions for a , here, a1 and a2 . Find the values of c1 and c2 which ensure that these values are obtained.