Home Experiment: Make a pendulum using a string about 25 cm (10") long, and a mass similar to a lemon (go ahead, use a lemon!). Now, hold the end of the string and vibrate it back and forth by 10 cm about three times per second, about once per second, and about once every three seconds. Carefully note the amplitude (how far the lemon swings) and the phase (is your hand out ahead of the lemon pulling it forward, or behind pulling it back?).

Now, compare the experiment you just did to the behavior of an RLC circuit as the driving frequency is increased.

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 sketched 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.