Chapter 17.3, Problem 2E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A spring with an 8-kg mass is kept stretched 0.4 m beyond its natural length by a force of 32 N. The spring starts at its equilibrium position and is given an initial velocity of 1 m/s. Find the position of the mass at any time *t*.

To determine

**To find:** The position of the mass at any time

Explanation

**Given data:**

The spring is stretched beyond its natural length, so

**Formula used:**

Write the expression for Hookeâ€™s Law.

Here,

Write the expression for Newtonâ€™s Second Law.

Write the expression for auxiliary equation.

Write the expression for the complex roots.

Here,

Write the expression for general solution of

Substitute

Substitute

Find the auxiliary equation using equation (3).

Solve for

Simplify

Compare equation (4) with equation (6).

Substitute

Since, the spring is start at its equilibrium position the value of

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