Cut off the wider end of a cork so that it measures 1/4 inch less than your needle.
Thread the needle with some nylon thread and tie a knot right next to the needle's eye. Run the needle from end to end through the center of the cork until the eye is just buried in it. This will keep the knot from coming undone. The cork should now look like a plumb bob with a needle for its tip.
Remove the lid from a large jar and mark the center of it on top. Use a hammer and punch to make a dimple in the metal where you marked it. This dimple makes a recess for the knot you're about to tie.
Use the hammer and drive a wire brad through the center of the dimple. Hold the wire brad with a pair of needle-nose pliers while puncturing the lid to avoid hitting your thumb.
Run the nylon thread through the underside of the lid through the hole you just made with the wire brad. Screw the lid on the jar with the cork on the inside. Adjust the length of the string so the tip of the needle is right next to the bottom of the jar, but not touching it. With that length of string, tie a knot large enough so that it can't pass through the hole. Add a little glob of silicone to seal the hole and to help further secure the knot. When the silicone dries, cut off the excess thread.
Remove the lid and cork from the jar and fill it with water. Place the cork in the water and screw the lid on tightly. Turn the jar upside down. The cork should float upward and look like an inverted plumb bob.
Put a drop of silicone in the center of the glass of what is now the top of the accelerometer (the bottom of the jar). When the silicone dries, it will keep the tip of your compass from sliding around. Using a fine-tip permanent marker and a compass, make a series of concentric circles. Start with a 1/4-inch radius and make each successive radius 1/4 inch larger than the last. Each one of these circles represents a magnitude of vibration or acceleration.
Place the accelerometer on a table and give the table an abrupt shove. The needle should move, indicating one of the circles at its maximum displacement. Larger vibrations cause the needle to reach circles with greater diameters. In this way, you can take relative measurements of vibrations.