How to Determine n for Quantized Energies in a Pendulum?

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SUMMARY

The discussion focuses on determining the integer value of n for quantized energies in a simple pendulum with a length of 0.6 m and a bob mass of 0.5 kg. The energy levels are defined by the equation En = (n + 1/2)hf0, where hf0 represents the quantization of energy. The user initially attempted to solve for n using the equation .0009(En+1) = En but encountered negative, non-integer results. After revising the approach to En+1 = En * 1.0001, the user calculated n to be approximately 9999.5, leading to the conclusion that n should be rounded to 10000.

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

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