Question

x¨+μ(x-2a)(x+a)+x=0,a>0 a fixed constant, It is known that a unique non-trivial periodic solution exists for large enough Determine the approximate maximum, minimum and period of this solution in the limit μ→+ infinity

Answer 1

The given equation represents the Duffing equation. A unique non-trivial periodic solution exists for large enough μ. The maximum, minimum, and period of this solution can be determined.

Step-by-step explanation:

The equation given, x'' + μ(x - 2a)(x + a) + x = 0, represents a non-linear second-order ordinary differential equation called the Duffing equation.

In the limit as μ approaches positive infinity, a unique non-trivial periodic solution exists.

The approximate maximum and minimum values of this solution can be determined by finding the roots of the equation for x'.

The period of the solution can be calculated using the formula for the period of a simple harmonic oscillator.