There are two major forces acting on the pendulum. One is the tension force that is upward toward the pivot point of the pendulum. The other is a restoring force acting directly downward toward the Earth or moon for that matter and is always constant.
So far, so good. These are indeed the two major forces, as you describe them. The problem comes with your understanding of how they are resolved:
These forces are not the same, so one of them must be resolved. The tension is always projected towards the pivot point and varies in magnitude. The restoring force is gravity of course. it is constant. It is gravity that is resolved.
Whilst you are correct that tension is always directed toward the pivot point, and that it varies in magnitude, the rest of what you say is very vague, and it is not entirely clear to me how you intend the forces to be "resolved". Here, though, is how I have been taught to resolve these forces:
When multiple forces are acting upon a body, they can be represented as vectors ("arrows" of force with both magnitude and direction, where the greater the magnitude, the longer the arrow). The
total effective force then - the resultant force which ultimately acts upon the body as though the body were subject to only a single force - is determined by summing up all of these vectors, which in visual terms amounts to placing them all head-to-tail and drawing a final vector from the tail of the first to the head of the last.
Here's how this works for a pendulum. First, let's identify the force vectors (I have "borrowed" the first diagram from
these lecture notes, which I otherwise haven't read, but they do look informative):
Here, the two vectors for the forces of gravity (mg) and tension (T) are shown, along with the effective force that this results in, Fnet. Here, as I described above, is how we arrive at that Fnet vector (I mocked this image up myself based on the above, and pretty roughly):
Here, we start by laying out the gravity vector, mg. Then, we place the tail of the tension vector, T, at the head of the gravity vector, and, to arrive at the effective resultant force - to "resolve" the forces as you put it - we sum these vectors by drawing a new vector from the tail of the gravity vector to the head of the tension vector.
Note that Fnet is on a tangent to the arc of the pendulum's swing at this point in its swing. In other words, at all times, the effective force on the pendulum acts along its arc. [Edit: My physics is a little rusty. I got this slightly wrong, as acknowledged in
this later post. The effective force points slightly upwards from the tangent, because as well as accelerating the pendulum along the tangent, it has to accelerate it upwards to change the tangent (centripetal force).] This can be proven, but for brevity and efficient use of energy I won't do that in this post.
What is the upshot of this? How does it relate to the competing claims in this thread?
It demonstrates that the effect of gravity - on the pendulum's downward motion - is, when the force of tension is also taken into account, to resolve into a force which accelerates the pendulum along its arc. The exact opposite is the case during the pendulum's upward motion. Gravity again resolves into a force along the pendulum's arc, but this time to
decelerate it (you can again draw a very similar diagram as the above which shows this). Here's the key point though: although the
directions of these forces are opposite,
the magnitudes of the forces at the opposite points in its arc are identical. In other words, the overall
acceleration due to gravity (when resolved with tension) is
identical to the overall
deceleration due to gravity.
This is why gravity does
not act to slow down the pendulum or dissipate its energy: the forces it exerts upon the pendulum over an entire oscillation (when resolved with the tension) are
equally balanced.
I'm not, but I'm open to your explanation as to how you think I am. Nothing that I've explained above would be at all controversial in a high school physics class (which I took).