OscillationsIntroduction
At the Dussehra mela in Mysuru, Riya climbs onto the big wooden jhula with Sina on her lap. The jhulawala gives them a gentle push and, when Riya begs for more, a hard one. The big swings feel much faster. But does each big swing really take less time than a small one? Or more? Riya decides to find out.
Back and forth, back and forth: a swing, a cradle, the pendulum of a wall clock, a boat bobbing at its mooring, the string of a sitar. A motion that goes to and fro about a middle position is an oscillation, and this chapter is about how to describe it, what keeps it going and how long each swing takes.
Pull the seat sideways and let go. The graph records the angle of the jhula as time passes.
The blue trace of your last swing and the grey trace of the one before cross the zero line at almost the same moments. A bigger swing has further to go, but it also moves faster, and the two effects very nearly cancel. A wave-shaped graph that repeats itself, here every 3.2 s, is the signature of an oscillation. By the end of the chapter you will be able to predict those 3.2 s from nothing but the length of the ropes.
The Plan for This Chapter
We start with periodic motion, any motion that repeats itself, and the words that describe it: period, frequency and displacement. Then comes the simplest and most important oscillation of all, simple harmonic motion (SHM), in which the displacement follows a sine curve. We will see it as the shadow of a particle going round a circle, work out its velocity and acceleration, find the force law that produces it, follow its energy, and finish with the simple pendulum that ticks inside old clocks.
Which of these is not an oscillation?
The fan blade repeats its motion on every turn, but it goes round and round, never to and fro about a middle position. Every oscillation repeats itself, but not every repeating motion is an oscillation. The next section makes this precise.