# How do you find time period of an oscillatory motion(not SHM)

1. Jan 29, 2012

### jd12345

1. The problem statement, all variables and given/known data
Force ( F ) = -kx /√( x^2 + r^2 ) where k is a constant and r(constant-amplitude) is the distance initially the object is away from the origin, x(variable) is distance of the object from the origin. Find time period of this oscillation

2. The attempt at a solution
Clearly Force is not proportional to distance so its not an SHM. For an SHM its easy to find time period - there is a simple formula but i have no idea how to do it for other oscillatory motions. I wrote acceleration as the second derivative of distance and then tried to integrate but its too lengthy and i got stuck in the integral too
IS there an easy method to find the time period of an oscillatory motion which is not an SHM
IS integrating the only way - if it is i'll have to post it in calculus section