Chapter 8.5, Problem 9AYU

Rework Problem 5 under the same conditions, except that at time $t=0$, the object is at its resting position and moving down.

To determine

To find: The solution by reworking Problem 5 under the same conditions, except that at time $\text{t} = 0$, the object is at its resting position and moving down.

Answer to Problem 9AYU

Solution:

$d = - 5\text{sin}\pi t$

Explanation of Solution

Given:

An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period $\text{T}$, Assume that the positive direction of the motion is up.

$a = 5; T = 2 seconds$

Formula used:

$d = a\text{sin}\left(wt\right)$

Calculation:

Here the object starts at vertical position $d = 0$, and moves downward.

$w = \frac{2\pi }{T},$

$d = a\text{sin}wt = a\text{sin}\frac{2\pi t}{T}$

$d = - 5\text{sin}\frac{2\pi t}{2}$

$d = - 5\text{sin}\pi t$