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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16.3, Problem 33E

Textbook Problem

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Motion of a Spring In Exercises 31-34, use the differential equation

which models the oscillating motion of an object on the end of a spring (see figure). In the equation, *y* is the displacement from equilibrium (positive direction is downward), measured in feet, *t* is time in seconds, *w* is the weight of the object, *g* is the acceleration due to gravity, *b* is the magnitude of the resistance to the motion, *k* is the spring constant from Hooke’s Law, and *F*(*t*) is the acceleration imposed on the system. Find the displacement *y* as a function of time *t* for the oscillating motion described subject to the initial conditions. Use a graphing utility to graph the displacement function.

To determine

**To calculate:** The displacement *y* as a function of time *t* for the oscillating motion described subject to initial condition. Also graph the displacement function using graphing utility. The given differential equation is

**Given information:**

The given differential equation is

**Concept Used:**

If

**Calculation:**

Consider the given differential equation is

The coefficients of the differential terms are,

Now putting these in the differential equation

The characteristics equation is

First, we have to find the solution of the characteristics equation

Therefore,

Let

Multivariable Calculus

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