Non-Linear Oscillator: Understand & Determine Ring Pendulum

[BlueDevil14]

Can someone please explain to me in layman's terms what a non-linear oscillator is? I need to determine if a ring pendulum is a non-linear oscillator, but I can't really do that without knowing what it is I am describing.

 

[Pythagorean]

Well, even a simple pendulum is a nonlinear oscillator. We only approximate for small angles that it's linear.

Ideal intro to physics springs are linear; their force goes as -kx, but a nonlinear spring might go as -kx^2.

Basically, any function that is a constant times a variable (like F=-kx) is linear. It allows for a lot of convenient things (like superposition).

anything that's a more complicated 'operator' on the variable is nonlinear. The operator can be multiplication by a constant (as in the linear case) or it can be squaring the variable, or the square root of the variable or the sinusoid of the variable, etc.

So nonlinear is a more general case, linear is a very special case.

 

[Andy Resnick]

Can someone please explain to me in layman's terms what a non-linear oscillator is? I need to determine if a ring pendulum is a non-linear oscillator, but I can't really do that without knowing what it is I am describing.

Nonlinear pendulums have an oscillation period that is a function of oscillation amplitude.