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As part of our quantum assignment we;ve to also look at a simple classical oscillator (it's part b to a question about the one dimensional harmonic oscillator). Problem is, I can hardly remember a thing that isn't to do wih quantum! So any help here would be appreciated. We've to find an expession for the velocioty of the particle as a function of positon, and I think I'm going okay with it, it's just the limits that I don't know about (maximum displacements are a and -a).

I've got it down to v(dv/dx)= (-w^2)x which gives me vdv=(-w^2)xdx, but I don't know which way to integrate between the limits. Is the amplitude at the bottom or the top? The example of it I looked at online as x as the upper limit and the amplitude as the bottom one, but I don't get that.....

Secondly, we've to (as a result fo the first bit), show that the probability of locating the particle in an interval dx between the maximum displacements a and -a is given by the ewt P(x)dx=dx/(pi(a^2 - x^2)^(1/2)). I'd like to take a stab at it but I don't know how to work out the probability for it - is it related to the probability that we use in quantum mechanics? Sorry, I sound so dumb here but I've no idea how to work out the probability. I've checked the net but to no avail. Please help (it would be much appreciated!)!

Claire

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# SHM and probabilities - help!

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