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## 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+1/2ayt

^{2}

a=-(w

^{2})x

a=9.8m/s

^{2}

mgyi+1/2mv

^{2}i=mgyf+1/2mv

^{2}f

## The Attempt at a Solution

i first solved for w using a=-(w^{2})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+1/2ayt

^{2}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.