How to Calculate Gravitational Potential Energy for a Swinging Toy?

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To calculate the gravitational potential energy (PE) of a 40 N toy in a swing with 2.0 m ropes, the relevant formula is PE = mgy, where y is the height relative to the lowest position. When the ropes are horizontal, the height is equal to the length of the rope, resulting in maximum potential energy. At a 30-degree angle with the vertical, the height can be calculated using the cosine of the angle to find the vertical displacement. At the bottom of the swing, the potential energy is zero since the height is zero. The discussion highlights the need for clarity in applying the gravitational potential energy formula in different positions of the swing.
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1. Homework Statement

A 40 N toy is placed in a light swing that is attached to ropes 2.0m long. Find the gravitational potential energy associated with the toy relative to its lowest position when (a) the ropes are horizontal (b) the ropes make a 30 degrees angle with the vertical and (c) at the bottom of the circular arc.

2. Homework Equations

PEg = mgy (note: y is distance)
Wg = -mg(yf-yi)=mgyi-mgyf=PEi-PEf
Wg=-deltaPE

3. The Attempt at a Solution

I do not know what to start. Well, as my prop show a similar problem with (b) problem, I tried to draw free body diagram. like vertical = y-axis and horizontal = x axis. So the the rope and y-axis makes a sort of triangle. and the unknown length of the one side of triangle must be length of cord multiplied by cos30. And I cant' go further. Maybe I went down all wrong. Will you help?
If I am asked solve the length between the maximum point reached by toy or something like that, I think I can do it. However, about energy, I am confused.
 
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At the bottom PE = ...?
a) The rope is horizontal. So the displacement is L ( length of the rope). So PE = ...?
b) The displacement is (L - Lcasθ). So PE =...?
 

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