A particle moves along the x-axis according to the $x = A (1 + sin ω t)$ $x = A(1+sinomegat)$ . What distance does it travel between t = 0 and $t = \frac{2.5 π}{ω}$ $t = (2.5pi)/omega$ ?

Question

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

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Answer 1 · 2018-04-20T08:11:48

5A

$x = A (1 + sin ω t)$ $x = A(1+sin omega t)$

This describes a harmonic oscillator with period $T = \frac{2 π}{ω}$ $T = (2 pi)/omega$ and amplitude A, oscillating about A.

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

$\frac{2.5 ω}{π} \equiv T + \frac{T}{4}$ $(2.5 omega)/pi equiv T + T/4$

In period $0 < t < \frac{5 T}{4}$ $0 < t < (5T)/4$ , it will travel a distance 5A.