Simple Harmonic Motion amplitude problem

[pondzo]

Homework Statement

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.

Homework Equations

x(t)=Asin(ωt)

The Attempt at a Solution

The correct answer is 2.49*10^-2sec

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 can't 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 don't 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.

 

[ehild]

Homework Statement

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.

Homework Equations

x(t)=Asin(ωt)

The Attempt at a Solution

The correct answer is 2.49*10^-2sec

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 can't use this method.

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

 

[pondzo]

Thank you for the quick reply ehild.

Wow, i can't believe i forgot about the inverse sine function on the normal calculators xD
thanks alot!

 

[ehild]

You are welcome

ehild

 

[HalfLostAndSearching]

I would recommend using the equation x(t) = A cos(ωt + ϕ), where ϕ is the phase angle, to solve this problem instead of the small angle approximation. This equation accounts for the phase shift of the object's motion and will give you a more accurate solution. You can solve for the phase angle by setting x = 0 at t = 0 and then using the given values of x and t to solve for ϕ. Once you have the phase angle, you can use it to solve for the time it takes for the object to go from x = 0.00 m to x = 7.00×10-2 m. Alternatively, you can also use the equation v(t) = -Aωsin(ωt + ϕ) to find the time at which the object reaches its maximum displacement of 7.00×10-2 m. I hope this helps.