# Simple Harmonic Oscillator

1. Feb 23, 2008

### Vuldoraq

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

$$U(x)=(cx^4)/4$$, 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 $$(s)$$

Units of potential energy are $$(kg*m^2)/(s^2)$$

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

$$(s)=\sqrt{((kg*m^2)/(s^2))}$$

in terms of the above equations this is,

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

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

$$T/4=\sqrt{((4*m)/(cA^2))}$$

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

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

Last edited: Feb 23, 2008