Calculating Time to Reach End of Tunnel in Earth's Centerless Tunnel

[lepori]

Homework Statement

suppose there is tunnel through the Earth which dose not cross center.
If the drop object in this tunnel, how many time it takes to reach end of tunnel?

earth is perfect sphere, there is no friction too
Giving data: Earth mass and radius

Homework Equations

The Attempt at a Solution

maybe low of energy conversation? :/ mgh = mv²/2

I had tried to use mathematical pendulums analogy,
but could not solve anyway p.s. we have to use school physics, no integrals and differentials

 

[haruspex]

I'm a little confused by the statement of the problem. If the tunnel does not go through the centre then it is not vertical, so an object 'dropped in' will hit the side. Maybe we have to assume it's sliding in a smooth tube.
You may not be expected to use calculus, but you will at least need to know something about simple harmonic motion. What have you been taught on that?
Draw a free body diagram for the object. What forces act on it? Find an expression for the force directing it to the midpoint of the tunnel when at distance x from that point.