# Equilibrium points of oscillations

#### Loonie

Joined Aug 30, 2011
17
1. Find the equilibrium points for the following equations. Determine whether these equilibrium
points are stable, and, if so, nd the approximate angular frequency of oscillation
around those equilibria.
(i) d2y/dx2(x) = cosh(x) (ii) d2y/dx2(x) = cos(x) (iii) d2y/dx2 (x) = tan(sin(x)):

Hello, I'd like to know if I am proceeding correctly for the very first question, 1i.
A solution to i would be a equilibrium point if it is a constant solution.
Therefore, d2y/dx2(x) = cosh(x) = 0;
When with this equation, I get x = i(pi) / 2
Am I going the correct way? Can i(pi) / 2 be an answer? I haven't got a complex number for a solution before...
After that, for stability, I would just look at points of x near i(pi)/2.

#### Loonie

Joined Aug 30, 2011
17
Can't seem to edit the first post so I am adding new information in another post. The question (in proper format) is in the MA1506.pdf.
Some advice would be much appreciated. Thank you

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#### amilton542

Joined Nov 13, 2010
497
It looks like you're trying to compute the stationary points of each function where the first derivative is equal to zero (equilibrium presumably) for a maximum or minimum value.

When you compute the second derivative and substitute the independent variable associated with the first derivative, this will determine if it is a maximum or minimum value by way of the operator.

I'm not sure if any of this will be useful for you, but it looks like you may need to work backwards and integrate the second derivative in order to determine the stationary points that could be regarded as a fixed value becuase the rate of change equates to zero.