# Total distance moved by particle from time t to time (t+100ms)?

A particle in the string oscillates with an amplitude of 13mm. At time t, the particle has zero displacement

How to calculate ‘total distance moved by the particle from time to time (t+100ms)?

### 1 Answer

- NCSLv 73 months ago
You'd need to know something more about the motion of the string, like its period (or frequency) or the full equation of motion.

y = 13mm * sin(2π*t/T)

where T is the period

gives you the amplitude at time t.

The particle will move through 4*13mm = 52 mm every complete cycle (up 13, back to 0, down 13, back to 0). So you need to know the number of complete cycles in 100 ms. Then you'd have to do some figuring for that fraction of a cycle that was left over.

If the period happens to be some integer multiple of 100 ms, then the total distance is simply

d = n*52 mm

where n is that integer.

Post an update if this answer is insufficient.