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## Homework Statement

a mass is placed on a loose spring and connected to the ceiling. the spring is connected to the floor in t=0 the wire is cut

a. find the equation of the motion

b. solve the equation under the initial conditions due to the question

## Homework Equations

## \sum F=ma

##

## x(t)=Asin(\omega t + \phi ) ##

## The Attempt at a Solution

a. due to the 2 law of newton: ## \sum F=ma_x

##

## mg-kx=ma ##

##

mg-kx=m\ddot{x}

\\

\ddot{x}=g-\frac{k}{m}x ##

b. first I'll find the point equilibrium

**##**

c-kx=ma

\\

c-kx=m\cdot 0

\\

x_0=\frac{c}{k}

##

c-kx=ma

\\

c-kx=m\cdot 0

\\

x_0=\frac{c}{k}

##

then I'll define ## y=x-x_0 ##

How do I go from here?

thanks