Motion of object (simple harmonic motion?)

[~christina~]

Homework Statement

A ball dropped from height 4.00m makes an ellastic collision with the ground. Assuming no mechanical energy is lost to air resistance.

a) show that the motion is periodic

b) determine period of motion

c) is the motion simple harmonic?

Homework Equations

not sure how to approach "showing motion is periodic" so I don't know what eqzn to use

The Attempt at a Solution

a) show that the motion is periodic...

How would I technically show that??

I do know that it would be periodic since the ball hits the ground then bounces back up to the height it was dropped from but as to showing that...

b) period of motion.

well the period would be the time interval for the particle to go through one full cycle of motion but I'm not sure what to use there as well since in the book all they explain is the period as $$T= 2 \pi / \omega$$

can anyone help me out?

Thank you very much

 

[andrevdh]

Try to draw a graph of position versus time for the motion of the ball (it drops, and rises, with a constant acceleration/deceleration) and see how long it takes for the graph to repeat itself.

 

[DylanB]

a) I'd suggest showing this with energy equations. conservation of mechanical energy will work.

b) You should look to your kinematic equations to find the time it takes to complete one cycle, down then back up again.

 

[~christina~]

thanks