The discussion centers on calculating the resultant displacement in a stretched spring, specifically addressing the vector sum of x and y components. The participants emphasize the importance of knowing whether dx and dy are equal, as well as the definitions of variables such as ##\lambda## and w. The correct approach involves understanding the tangent function in relation to triangles, where tangent equals 1 only when x equals y. Without clear definitions and context, the equations provided (x = acos(2*pi*z/lambda - 2*pi*w) and y = a sin(2*pi*z/lambda - 2*pi*w)) remain ambiguous.
PREREQUISITESStudents studying physics, particularly those focusing on mechanics and wave motion, as well as educators looking to clarify concepts related to vector sums and trigonometric functions in real-world applications.
tina21 said:If I take the vector sum, I am getting the angle to be 1. (tan^-1 tan(1)). Is that correct?
thanks for your help :)DEvens said: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.
thanksBvU said: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.
An equation is meaningless without a definition of the variables in it and the context in which it applies. What are the variables here, and what is the context?tina21 said:Homework Equations: x = acos(2*pi*z/lambda - 2*pi*w)
y = a sin(2*pi*z/lambda -2*pi*w)