Calculating ∅ in Simple Harmonic Motion Equation x = xo + Asin(ωt + ∅)

[pvpkillerx]

x = x_o + Asin(ωt + ∅)
I know all of the values, except for ∅.
But i don't know how to get the value for ∅


The attempt at a solution:
0.349 = 0.367 + 0.413Sin(8.5 * 0.8938 + ∅)
-0.018 = 0.413Sin(7.5973 + ∅)
-0.04358 = Sin(7.5973 + ∅)
From here on, i am confused, I tried using the trigonometric identities.
-0.04358 = Sin7.5973Cos∅+Cos7.5973Sin∅
-0.04358 = 0.1322Cos∅ + 0.9912Sin∅
And once again, i am stuck. I don't know what to do, to get ∅. Please help, thanks.

 

[Simon Bridge]

1. solve the equation for phi *before* substituting the values.
2. substitute the values

the opposite of sine is arcsine, on your calculator it is sin^-1 and is often accessed using [inv]+[sin] or similar, so:

arcsin(x-x0)-wt=\phi

 

[collinsmark]

x = x_o + Asin(ωt + ∅)
I know all of the values, except for ∅.
But i don't know how to get the value for ∅The attempt at a solution:
0.349 = 0.367 + 0.413Sin(8.5 * 0.8938 + ∅)
-0.018 = 0.413Sin(7.5973 + ∅)
-0.04358 = Sin(7.5973 + ∅)
From here on, i am confused, [...snip...]

Take the inverse sine of both sides of the equation. The inverse sine is sometimes called ARCSIN, Arcsin, asin, Asin, ASIN, arc sine, or sin^-1().

Your calculator should have this function. If not, maybe your computer's calculator has it. For example on Windows 7, go to the accessories start menu folder, and open the calculator. Click on View / Scientific. Select either radians or degrees, depending one which units you are working with for this problem. Enter the "-0.04285" value. Click the inverse button. Then click on sin^-1.

 

[pvpkillerx]

Thanks, i feel stupid now (: Can't believe i didn't see that. Thank you!

 

[Simon Bridge]

trig functions can be intimidating - a lot gets hidden in those letters.

 

[xnitexlitex]

I'm having a similar problem. I need to find the phase constant for the function
x(t) = A(cos ωt + phi) so that I can find x when t = 0. When t = 2, x = 0.125. I found the amplitude, but I need the phase constant.

My values: 0.125 = 0.528 cos [(6.75)(2) + phi]

The attempt at a solution
I multiply 6.75 by 2 to get 13.5: 0.125 = 0.528 cos (13.5 + phi)
I then divide by 0.258: 0.23674 = cos (13.5 + phi)
At that point, I don't know what else to do. Any help would be appreciated.

 

[Simon Bridge]

Your next step is to take the inverse cosine of both sides.
This is called arccos or cos^-1.

cos^-1(0.23674) = 13.5 + phi

it is the acos function in gnu-octave and is accessed via [inv]+[cos] on most scientific calculators.