Q17. - Algebra 2

Question

PHYSICS

For Exercises $16-18$, use the following information.

A weight is attached to a spring and suspended from the ceiling. At equilibrium, the weight is located 4 feet above the floor. The weight is pulled down 4 foot and released.

Write the equation for the height h of the weight above the floor as a function of

time $t$ seconds.

Step-by-Step Solution

Answer

The equation is $h=4-\cos \frac{\pi }{2}t$

Step 1. Given information

A weight is attached to the spring as shown in figure.

Step 2. Concept used

First we know the amplitude of the motion. Find the value of angular frequency and put in the general equation.

Step 3. Calculation

The general equation is-

$y=A\cos \omega t$

But here we take the reference as ground and the amplitude is one foot.

Now, the value of angular frequency is

 $\begin{array}{l}\omega =\frac{2\pi }{t}\\ \omega =\frac{2\pi }{4}\\ \omega =\frac{\pi }{2}\end{array}$

The equation is-

 $h=4-\cos \frac{\pi }{2}t$