# Resultant displacement in a stretched spring

#### tina21

Homework Statement
a stretched spring is given simultaneous displacement in the x and y directions. what is the resultant displacement and angle ?
Homework Equations
x = acos(2*pi*z/lambda - 2*pi*w)
y = a sin(2*pi*z/lambda -2*pi*w)
If I take the vector sum, I am getting the angle to be 1. (tan^-1 tan(1)). Is that correct?

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#### BvU

Homework Helper
Hi,
Your homework problem statement looks deficient to me: it does not say whether dx and dy are equal or not, there is no mention of $\lambda$ or w, no mention of the orientation of the spring, etc.

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#### DEvens

Gold Member
If I take the vector sum, I am getting the angle to be 1. (tan^-1 tan(1)). Is that correct?
No, that's not correct. I think I can guess what you are trying to say but I have to guess. I think you mean that the x and y are equal, so you want to get the angle that comes from that.

But remember what tangent is in terms of triangles. Opposite over adjacent. Or if you like to build a roof, rise-over-run. So the tangent is 1 if x=y. You don't want to take the tangent of 1 since that's already a tangent.

But the question does not say x=y. So what is the tangent if x is not equal to y?

Also, you need to get the resultant displacement. Remember how you calculate distances if you have the x and the y.

#### tina21

No, that's not correct. I think I can guess what you are trying to say but I have to guess. I think you mean that the x and y are equal, so you want to get the angle that comes from that.

But remember what tangent is in terms of triangles. Opposite over adjacent. Or if you like to build a roof, rise-over-run. So the tangent is 1 if x=y. You don't want to take the tangent of 1 since that's already a tangent.

But the question does not say x=y. So what is the tangent if x is not equal to y?

Also, you need to get the resultant displacement. Remember how you calculate distances if you have the x and the y.

#### tina21

Hi,
Your homework problem statement looks deficient to me: it does not say whether dx and dy are equal or not, there is no mention of $\lambda$ or w, no mention of the orientation of the spring, etc.
thanks