(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi,

For a certain oscillator the net force on a body, with mass m, is given by F=-cx^3.

One quarter of a period is the time taken for the body to move from x=0 to x=A (where A is the amplitude of the oscillation). Calculate this time and hence the period.

2. Relevant equations

[tex]U(x)=(cx^4)/4[/tex], where U(x) represents the potential energy of the body.

3. The attempt at a solution

In order to solve this I used a homogeneity of units argument as follows,

Units of time are [tex](s)[/tex]

Units of potential energy are [tex](kg*m^2)/(s^2)[/tex]

In order to get from the potential energy units to the time units,

[tex](s)=\sqrt{((kg*m^2)/(s^2))}[/tex]

in terms of the above equations this is,

[tex]\sqrt{(m*x^2/U(x))}[/tex]=[tex]\sqrt{((4*m*x^2)/(c*x^4))}[/tex]

let x=A and the equation =T/4,

[tex]T/4=\sqrt{((4*m)/(cA^2))}[/tex]

hence, [tex]T=4*\sqrt{((4*m)/(cA^2))}[/tex]

However this is incorrect, my answer is wrong by a multiplicative factor. Please could someone show me where I have gone wrong?

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# Homework Help: Simple Harmonic Oscillator

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