
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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22.In the absence of damping, the motion of a spring–mass system satisfies the initial value problem
mu′′+ku=0,u(0)=a,u′(0)=b
a.Show that the kinetic energy initially imparted to the mass is mb2/2 and that the potential energy initially stored in the spring is ka2/2, so initially the total energy in the system is (ka2 + mb2)/2.
b.Solve the given initial value problem.
c.Using the solution in part (b), determine the total energy in the system at any time t. Your result should confirm the principle of conservation of energy for this system.
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