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