Question 8: What is total distance covered by a simple harmonic oscillator in a time equal to its period? The amplitude of oscillation is A.
Distance covered by the oscillator in one period
The distance between the mean position and extreme position is called amplitude of the oscillation. In the adjacent figure, it is from Z to X or Z to Y. When the oscillator oscillates, it goes from one extreme to another and then back to the same point in one time period time.
Now let the oscillator is at point X as it oscillates. It goes from X to Y via mean position Z. Therefore, reaching point Y, it covers a distance A + A = 2A.
It is then returns from that point and goes to X again, covering the same distance 2A. When it reaches X again, its one period time is completed.
Therefore, the oscillator covers a distance of 4A in one period time.