Chapter 8.5, Problem 8AYU

In Problems 5-8, 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 $T$, write an equation that relates the displacement $d$ of the object from its rest position after $t$ seconds. Also assume that the positive direction of the motion is up.

$a=\text{4};T=\frac{\pi }{2}$ seconds

To determine

To find: An equation that relates the displacement $\text{d}$ of the object after $\text{t}$ seconds from its rest position

Answer to Problem 8AYU

Solution:

$d = - 4\text{cos}4t$

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.

$a = 4; T = \frac{\pi }{2} seconds$

Formula used:

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

Calculation:

Here the object relates the displacement after $\text{t}$ seconds from its rest position.

$a = - 4$ and it moves upward.

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

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

$d = - 4\text{cos}\frac{2\pi t}{\pi /2}$

$d = - 4\text{cos}4t$