Not as far as you'd think from what real rocket scientists think is possible. Space Elevator

I think there is a basic misconception of the forces involved. The orbit point is not a static fixed point that could support the swing of a massive element underneath. It would be a problem merely to keep the space elevator stable. A swinging weight beneath would destabilize the whole system and it most likely would fall, or at minimum, disintegrate in a spectacular manner.

Even if you can build the contruption, the pendalum swings down (into the sea and earth) before it comes up. I don't get it. You could not build one to go between to points which are one mile apart and you need a trench. Am I missing something?

The trench concept has been explored froma different point of view. If a straight tube could be built between two distant points on the surface of the Earth and the tube evacuated to prevent air resistancefrom causing drag on a vehicle, an unpowered vehicle on wheels would roll downhill for half the journey and acquire enough velocity to roll uphill on the other half of the journey to a dead stop at the end. And no matter how long the tube, all journeys (even through the center of the Earth) would take the same time. Unfortunately,our primitive engineering capabilities are not up to constructing this simple economic system.

The idea and related schemes have been around for over a century. The simplest is a cable stretching up to a ballast weight higher than geosynchronous orbit, with the lower end firmly anchored to the Earth's crust; since the ballast is travelling faster than orbital speed, it exerts a continuous pull on the retaining cable. Presumably, a small Near Earth asteroid is captured and used as the ballast. In the event of cable structure failure, the ballast is flung off into space by inertia.

In practice, a capsule would ascend the cable to the geosynchronous orbit altitude, roughly 22,000 miles; at that point it would release and become an independant spacecraft.

The pendulum idea does away with an anchor; the ballast is stationed at the geosynchronous orbit, with several cables attached; as the assembly spins, the cables dip into the atmosphere in succession, pulling up capsules or delivering them to the surface.

As the ballast/cable assembly spins, the 22,000 mile long cables sweep to an altitude of 44,000 miles before descending.

All we need for this is several hundred thousand miles of Larry Niven's "Sinclair molecular chain," a few "antigravity sleds," and a conveniently sized Near-Earth asteroid (nickel-iron preferred).

See Skyhook, Lofstrom Loop, Space Fountain, Space Elevator.