# Investigation The differential equation 8 32 y " + b y ' + k y = 8 32 F ( t ) , y ( 0 ) = 1 2 , y ' ( 0 ) = 0 models the oscillating motion of an object on the end of aspring, where y is the displacement from equilibrium (positivedirection is downward), measured in feet, t is time in seconds, b is the magnitude of the resistance to the motion, k is the spring constant from Hooke’s Law, and F ( t ) is the accelerationimposed on the system. (a) Solve the differential equation and use a graphing utility tograph the solution for each of the assigned quantities for b , k , and F ( t ). b = 0 , k = 1 , F ( t ) = 24 sin π t b = 0 , k = 2 , F ( t ) = 24 sin ( 2 2 t ) b = 0.1 , k = 2 , F ( t ) = 0 b = 1 , k = 2 , F ( t ) = 0 (b) Describe the effect of increasing the resistance to motion b . (c) Explain how the motion of the object changes when astiffer spring (greater value of k ) is used. ### Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378 ### Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378

#### Solutions

Chapter 16, Problem 56RE
Textbook Problem

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