Coupled pendulums and wave equation.

[HenryA.]

Homework Statement

(A)
[PLAIN]http://remote.physik.tu-berlin.de/farm/uploads/pics/Gekoppeltes_Pendel_01.png
What happens when you swing pendulum P1?

(B)
How does the position of the spring affect the outcome?

(C)
If the length of the string of one pendulum was longer than the other, what will happen when you start swinging either one of these pendulums?

(D)
This an equation for describing a wave:

$$S(x,t)=Sm \times sin \left(\frac{2\pi}{T}t-\frac{2\pi}{\lambda}x\right)$$

Sm = amplitude

How do you derive this part:

$$\left(\frac{2\pi}{T}t-\frac{2\pi}{\lambda}x\right)$$

The Attempt at a Solution

(A)
When pendulum P1 starts swinging and it reaches its maximum (the amplitude) at π/2, the other pendulum starts moving, . At this point the energy is starting to get transferred from P1 to P2. Once P1 stops moving, P2 will have reached its maximum amplitude. At this point P2 overtakes P1 by π/2 and the whole process starts again.
(B)
Slower.
(C)
In the experiment, one of them never stopped moving, the other one started and stopped multiple times. I know that these two pendulums have different frequencies, but I do not know how I would describe this phenomenon.
(D)
I got nowhere with this question.

 

[HenryA.]

Another question:

What formula could I use to describe the states of energy of those two pendulums, specifically referring to the point where they have they same amplitude.