Home Experiment: Make a pendulum using a string 1 to 1.5 meters long (40-60 inches), and a mass similar to a lemon (go ahead, use a lemon!). This will give you a pendulum with a resonant period in the range 2 to 2.5 seconds (T = 2{L/g}^1/2). In terms of frequency, f = 1/T, so the resonant frequency is between 0.5 and 0.4 Hz.

Now, hold the end of the string and vibrate it back and forth by 5 cm, slowly varying the frequency of your oscillation. When you find the right frequency, the lemon will swing back and forth with quite a large amplitude. This is the resonant period for your pendulum. Note the phase between the motion of your hand and the lemon (is your hand out ahead of the lemon pulling it forward, or behind pulling it back).

Try swinging the lemon a little more slowly (longer period than at resonance), how does the amplitude change? How about the phase?

Next, try going a little more quickly than at resonance. What happens to the amplitude and phase now?

Finally, compare the experiment you just did to the behavior of an RLC circuit.

A radio has RLC circuits inside that oscillate at the same frequencies as the radio waves they receive (88.1-107.9 MHz for FM, 540-1180 KHz for AM). Select values of L and C that could be used to make these circuits.

An inductor or a capacitor in an ac circuit has a (time varying) current flowing through it and voltage across it. However, the average power P_AV = 0. Explain how this works out, recalling that power is equal to voltage times current.

Old radios used to tune from one frequency to another using variable capacitors like the one shown here. In such a device there are two rows of semicircular plates. One set of plates (all electrically connected together) are fixed to the base, and the other set (all connected together) can rotate through a half turn. At one extreme they are opposite to the fixed set, and at the other extreme they are fully "interleaved" with the fixed set.

Assuming the whole thing must fit inside an old radio, estimate the maximum capacitance.

Hint: for ten fixed and ten rotating plates, you can treat this as 10 parallel plate capacitors in parallel.