Show that the equation has no (real-valued) solution.
has no (real-valued) solution.
Now from Step 1, this is clear that the value of is not real.
Thus has no (real-valued) solution.
Pendulum with Varying Length. A pendulum is formed by a mass m attached to the end of a wire that is attached to the ceiling. Assume that the length l(t)of the wire varies with time in some predetermined fashion. If
U(t) is the angle in radians between the pendulum and the vertical, then the motion of the pendulum is governed for small angles by the initial value problem where g is the acceleration due to gravity. Assume that where is much smaller than . (This might be a model for a person on a swing, where the pumping action changes the distance from the center of mass of the swing to the point where the swing is attached.) To simplify the computations, take g = 1. Using the Runge– Kutta algorithm with h = 0.1, study the motion of the pendulum when . In particular, does the pendulum ever attain an angle greater in absolute value than the initial angle ?
94% of StudySmarter users get better grades.Sign up for free