# Thread: Second Order Spring Application Problem

1. ## Second Order Spring Application Problem

A spring is stretched 2 inches by a 3-lb weight. The weight is pushed up 3 inches above equilibrium and released. Give the equation of motion.

I know it is an easy question, but I am not exactly sure the proper way to answer this things. Thanks guys.

2. Assumptions:

We will take the new equilibrium position as y= 0
and points above it are -ve and below it are positive

Steps:
---------
We will use
SHM's equation
given by

$y= A sin(\omega t + \phi )$
-----------
1) use equation

kx= mg
to get value of k, x here is 2inch

2)
Here since the block is initially above the new equilibrium position so we will
have phase constant

$\phi = \frac{-\pi}{2}$

and

3) Angular frequency is given by
$\omega = \frac{k}{m}$

4) A here stands for amplitude its = 3inch in your question

______________

That's how I do it.

Incase if you use any other position as Y = 0 than add a constant "c" in SHM's equation
Where

c will be given by the displacement of this new position from the equilibrium position.