# Ball dropped, elastic collision, harmonic motion

## Homework Statement

A ball dropped from a height of 4m makes a perfectly elastic collision with the ground. Assuming that no energy is lost due to air resistance.
show the motion is periodic
determine the period of the motion

## Homework Equations

yf-yi=vit+1/2ayt2
a=-(w2)x
a=9.8m/s2
mgyi+1/2mv2i=mgyf+1/2mv2f

## The Attempt at a Solution

i first solved for w using a=-(w2)x and got w=2.2rad/s i then solved for T using T=2pi/w and got T=2.86s
i divided T by 4 to obtain t or time to max extension and got t=.9 sec
i also used the equation yf-yi=vit+1/2ayt2 and solved for t getting 2.86s???? this is confusing because i set vi=0 yf=0 yi=4 and solved for t. I would expect that t be half of T since this would be the time from 4m to the ground.