Given the approximationshow that the equation of motion for the mass m when it is released...

Given the approximation

show that the equation of motion for the mass m when it is released from rest at x = x0from the slingshot can be written as

where

Assume that the cords connecting the mass to the slingshot are linear springs with spring constant k, length L, and unstretched length L0. Ignore gravity and assume L > L0. Equation (2) is a famous differential equation in mechanics called Duffing’s equation.

Figure P3.37