I don’t see where you’re coming from. Just because the pendulum is moving does not mean it generates gravitional waves.
I’m no expert on gravitational waves, but SHM can parameterized by 1 parameter which makes me suspect that no gravitational waves are being generated.
Any source with a time-varying quadrupole moment will radiate some amount of gravitational radiation; this does in fact include an object in SHM.
This statement is still correct, though. I just ran through the numbers, and I found that a 10-gram pendulum swinging back & forth with amplitude 1 cm at the end of a 30-cm pendulum radiates about 10[sup]-60[/sup]watts of energy in the form of gravitational waves. If it continued to radiate its energy only in this form, at this rate, it would run out of energy in just 10[sup]47[/sup] years. For comparison, this about 10,000,000,000,000,000,000,000,000,000,000,000,000 times longer than the current age of the Universe (give or take an order of magnitude.)
>If it continued to radiate its energy only in this form, at this rate…
Nicely done, MikeS!
It wouldn’t continue to radiate at that rate, though. It would radiate at a rate that was proportional to the amplitude, so the amplitude would decay with a relaxation time of the time period you quote. Every 10^47 years, the amplitude would be smaller by the ratio 1/e.
Tidal forces in the pendulum and the planet would eventually stop it.
But wouldn’t that be called friction?
And where in the OP does it say this pendulum is on a planet?
Yes, I think it would, but then again you can have it converted to kinetic energy if the substance is water, or elastic and inelastic deformations are also possible,
Well it has to be gravitationally bound to something, planet, star, moon, perhaps there would be no tidal forces if it was bound to a black hole in the black hole itself, though the tidal forces would still be in the pendulum.
According to Einstein, acceleration and gravity are equivalent. It could be on an accelerating object which would not be subject to tidal or coriolis forces (or a planet not rotating about its own axis).
I’m not sure what you mean by tidal forces. Do you mean the interaction between the object supplying the gravity and the pendulum, even if not physically touching?
I interpret the OP to ask, “in the total absence of any other forces, subject only to the force necessary to cause a pendulum to cycle, would the cycle ever die out?”
For a point only, gravity would act on 2 points slightly differently due to the distance and angle to the gravitationally bound object
The internal forces that developed inside both objects due to the gravitational force between them. The earth/moon is a example. The moon is however gravitationally locked, so any tidal force would be small and just tend to stabilize the lock (but still there). In the earth we have ocean tides which is caused by the gravity of the moon (the soild earth also has tides, but the oceans are easier to see), the tides are caused by energy ‘stolen’ from the earth-moon system causing a drag, a new energy loss as the energy is converted to kinetic energy of the oceans, then to heat through frictional losses.
This would be true for a material such as titanium. However, other materials, such as steel, do not exhibit an endurance limit, and therefore, would not fail in the manner suggested.
This is getting down to the point where the occasional collision with a neutrino becomes significant.
0.000079 electron volts = 1.2657194 × 10^-23 watts second
Unless you shield against neutrinos, the pendulum will swing chaotically, forever.
Cheers 
General relativity is the most beautiful theory in physics by a mile. I suppose howver which way you frame it SHM does not occur in stationary spacetime.
You all are making me laugh. The OP asks for “basic physics help” and gets answers full of nuances of material science and quantum gravitational effects.
Basically, in a classical sense, if there are no forces acting on the pendulum than gravity, it will swing forever. The amount of potential energy at the top of the swing, where the velocity is zero, is exactly the same amount of kinetic energy when the pendulum is at the bottom where the velocity is maximized.
Each little bit of potential energy is traded into greater and greater velocity as the pendulum swings “downhill.” As it swings “uphill,” each little bit of kinetic energy is traded back to potential. At any one point the sum of the kinetic and potential energies is exactly the same. Since, by definition of the problem, there is no other force dissipating energy in the pendulum, it will swing forever.
Of course, there is no way it could ever be built under any conditions, but the OP was asking about the basic relationship between velocity and gravity in a classical pendulum problem.
Thanks,** Mr. E.** I had to deduce that from all the theoretical blah blah that followed my OP. That’s exactly what I was asking, and I thank you for answering it. I asked what time it was, and was told how to make a watch.