# Resultant displacement in a stretched spring

• tina21
In summary: 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. You want to take the tangent of 1 (which is already a tangent), so you should replace tan^-1 with tan.
tina21
Homework Statement
a stretched spring is given simultaneous displacement in the x and y directions. what is the resultant displacement and angle ?
Relevant 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?

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.

Last edited:
Delta2
tina21 said:
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.

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.

BvU 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.
thanks

tina21 said:
Homework Equations: x = acos(2*pi*z/lambda - 2*pi*w)
y = a sin(2*pi*z/lambda -2*pi*w)
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?

## What is resultant displacement in a stretched spring?

Resultant displacement in a stretched spring refers to the total distance that the spring has been stretched from its original length when a force is applied to it.

## How is resultant displacement calculated in a stretched spring?

The resultant displacement in a stretched spring can be calculated by measuring the change in length of the spring from its original length to its stretched length.

## What factors affect the resultant displacement in a stretched spring?

The resultant displacement in a stretched spring is affected by the magnitude of the applied force, the stiffness or spring constant of the spring, and the initial length of the spring.

## What is the relationship between applied force and resultant displacement in a stretched spring?

The resultant displacement in a stretched spring is directly proportional to the applied force. This means that as the force increases, the resultant displacement also increases.

## Can the resultant displacement in a stretched spring be negative?

Yes, the resultant displacement in a stretched spring can be negative if the spring is compressed rather than stretched. In this case, the spring is returning to its original length and the displacement is in the opposite direction of the applied force.

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