# Simple Harmonic Motion problem

**1. The problem statement, all variables and given/known data**

An object is undergoing simple harmonic motion with frequency f = 3.1 Hz and an amplitude of 0.15 m. At t = 0.00 s the object is at x = 0.00 m. How long does it take the object to go from x = 0.00 m to x = 7.00×10^{-2} m.

**2. Relevant equations**

x(t)=Asin(ωt)

**3. The attempt at a solution**

The correct answer is 2.49*10^{-2}sec

ω=2[itex]\pi[/itex]f=6.2[itex]\pi[/itex]

so, i set the following equation: 0.07=0.15sin(6.2[itex]\pi[/itex]t)

but i can not solve it without the solving capabilities of a graphics calulator, so i cant use this method.

i then set up a similar equation using small angle approximation but in order to get it to the right accuracy i need to include the second term (ie sinθ=θ – θ^{3}/6

but this then turns it into a cubic function (which i dont have the level of math to solve)

Is there a different way to go about this question that i am missing?

thank you in advance, Michael.

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