Question

A particle moves along the x-axis according to the `x = A(1+sinomegat)`. What distance does it travel between t = 0 and `t = (2.5pi)/omega`?

options given:
a. 6 A
b. 4 A
c. 5 A
d. none

Answer 1

5A

Explanation:

`x = A(1+sin omega t)`

This describes a harmonic oscillator with period `T = (2 pi)/omega` and amplitude A, oscillating about A.

ie In period `0 < t < T` it will travel a distance 4A.

`(2.5 omega)/pi equiv T + T/4`

In period `0 < t < (5T)/4`, it will travel a distance 5A.