Measuring the dampening sinusoidal wave of a simple LC Tank circuit?
Try this:

1) Set the scope to single-sweep at a trigger level of about half of your supply voltage.

2) Connect one end of the capacitor, one end of the inductor, the scope ground, and the power supply ground together.

3) Connect the scope probe hot to the other end of the inductor, but let the cap float.

4) Arm the scope.

5) Momentarily connect supply hot to the floating end of the cap in order to charge it.

6) Disconnect the supply from the cap and, while watching the scope screen, touch the floating end of the cap to the end of the coil connected to the scope probe.

7) You should see the damped oscillation.

If you don't, make sure that your scope is triggering properly, that you've got the sweep speed and amplitude settings right, and that you've got the brightness cranked high enough to let you see a single sweep. 

Just for grins, here's a link to an LTspice simulation.