Harmonic Oscillator grandfather clock

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Homework Statement

The pendulum of a grandfather clock has a period of 1s and makes excursions of 3cm either side of dead centre. Given that the bob weighs 0.2kg, around what value of n would you expect its non negligible quantum amplitudes to cluster?

Homework Equations

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The Attempt at a Solution

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I think the n here refers to the nth energy eigenvalue so En = (n + 1/2) h/2pi w

How do i work this out? My guess is that I need to work out the energy of a classical harmonic oscillator and equate this to (n+1/2) h/2pi w to get n?

So i know w = 2pi .. I've worked out the total energy of the classical oscillator to be 3.5 x 10^-3 J (using the fact that at max amplitude total energy = pe)

Then i equated this to (n+1/2)h/2pi w and got n = 5.3 x 10^30..

Is this right?

Thanks

Thanks!

 

[Andrew Mason]

Your calculations of pendulum energy and of n are correct.

AM