How to Determine n for Quantized Energies in a Pendulum?

[w3390]

Homework Statement

A simple pendulum has a length equal to 0.6 m and has a bob that has a mass equal to 0.5 kg. The energy of this oscillator is quantized, and the allowed values of energy are given by En = (n + 1/2)hf0, where n is an integer and f0 is the frequency of the pendulum. Find n such that En+1 exceeds En by 0.010 percent.

Homework Equations

En=(n+1/2)hf0

The Attempt at a Solution

I thought this sounded like a simple algebra problem, so I set .0009(En+1)=En and solved for n after plugging in the equations. I know there is something wrong with this equation because I keep getting negative, non-integer values for n but I cannot figure out what is wrong. Any help is greatly appreciated.

 

[w3390]

Since my first post, I have tried a revised approach. This time I have En+1=En*1.0001. This gives me (n+1)+(1/2)=(n+(1/2))1.0001. After doing all the algebra, I am getting 9999.5 as my answer for n. Since the question asks for an integer value, I do not know if show input 9999 as my answer or if my answer is just wrong in general.

 

[gabbagabbahey]

Your second method looks fine, and I would round 9999.5 up to 10000.