# Homework Help: SHM question involving a tunnel through earth

1. Sep 27, 2011

### craig.16

1. The problem statement, all variables and given/known data
A tunnel is bored through the centre of the Earth from Liverpool to New Zealand and a travel pod is dropped into it. The gravitational force on the pod is proportional to its distance from the centre of the Earth and so it undergoes simple harmonic motion described by

z=R0cos$\omega$t

where

z=position relative to the centre of the Earth
$\omega$=1.2*10-3rads-1

1) What is the velocity of the pod when it reaches the centre of the Earth?

2) How long does the pod take to travel to the opposite side of the Earth?

2. Relevant equations
The one displayed above

3. The attempt at a solution
For question 1) since its at the centre of the Earth z=0 giving:
0=R0cos$\omega$t
cos$\omega$t=0
$\omega$t=1
t=1/$\omega$
and thats where I hit a dead end. I know my approach is completely wrong since the end result for velocity is faster than the speed of light however I don't know exactly how to remedy this situation. Any hints will be greatly appreciated as this is frustrating me how I can't answer a basic SHM question like this.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 27, 2011

### SammyS

Staff Emeritus
I don't see how you calculated velocity at all.

What did you get for the time to reach the center of the Earth?

What's the period of this motion?

What is dz/dt as a function of t?

3. Sep 28, 2011

### craig.16

Doesn't matter, I worked it out now. Thanks for the reply anyway.