# Simple Harmonic Motion amplitude problem

1. Mar 1, 2014

### pondzo

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

ω=2$\pi$f=6.2$\pi$
so, i set the following equation: 0.07=0.15sin(6.2$\pi$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 - θ3/6
but this then turns it into a cubic function (which i dont have the level of math to solve)

2. Mar 1, 2014

### ehild

You need a simple scientific calculator only. What is sin(6.2πt)? With inverse sine, (and setting the calculator to radian mode), get the angle θ=6.2πt.

ehild

3. Mar 1, 2014

### pondzo

Thank you for the quick reply ehild.

Wow, i cant believe i forgot about the inverse sine function on the normal calculators xD
thanks alot!

4. Mar 1, 2014

### ehild

You are welcome

ehild