Spring Walkthrough for Programmers Struggling With Math

[mctuble]

I'm a programmer who loves math but unfortunately is not all that good at it. I'm trying to model a simple spring to be used as a form of suspension later on. Imagine I have:

Vector* p1;
Vector* p2;

float restLength;
float damping;
float stiff;

p1 and p2 obviously being vectors holding x and y coordinates for each along with a mass variable for each. The other three are pretty self explanatory

So I know Force = -stiff * distance(p1,p2) - damping * v

I have a bunch of questions about that. Is Force a vector? if so does that mean I wouldn't use the distance formula to find the distance? instead just subtract the x's and y's and put that in a vector? Also I'm confused as to what v is... I read its "v is the relative velocity between the two points connected by the spring" which I don't quite understand.

So bottom line is I want to take 2 points connected with a spring, each with potentially a different mass and with variables for restLength, damping, and stiffness and calculate the position of the spring for the next iteration.

If someone could walk me through this while breaking down the math to the basics (preferably without the mention of a vector) I'd be very thankful. I can understand the basic concept of what is happening I just can't understand the formulas that well. I've searched every site I can find but I can't really get off the ground. Please help. Thanks in advance.

 

[LightHero]

The force equation you provided is a vector equation, meaning that it is composed of two components (x and y). The distance between the two points, p1 and p2, is also a vector, so you would need to use the vector distance formula to calculate it. The velocity, v, is the relative velocity between the two points connected by the spring. This means that you would need to calculate the velocity of each point relative to the other. To do this, you would need to calculate the difference between the positions of the two points in the previous iteration and the current iteration, and then divide this by the time step. Once you have all these values, you can calculate the force vector on each point, which will give you the direction and magnitude of the force. You can then use this force to calculate the acceleration of each point, and then the new position for each point in the next iteration.

 

[astrokreng]

I understand that math can be challenging for some individuals, but it is an important tool in many fields, including programming. It is great that you have a love for math and are trying to improve your skills. I am happy to assist you in understanding the concepts behind your spring model.

First, let's start with the formula you provided: Force = -stiff * distance(p1,p2) - damping * v. This is known as Hooke's Law, which describes the force exerted by a spring. Yes, Force is a vector quantity, meaning it has both magnitude and direction. In this case, it represents the force exerted by the spring on the two points, p1 and p2.

The distance formula is used to find the distance between the two points, which is necessary in calculating the force exerted by the spring. So, you would still use the distance formula to find the distance between p1 and p2.

Now, let's talk about v. In this formula, v represents the relative velocity between the two points connected by the spring. Velocity is a vector quantity that describes the rate of change of an object's position. In this case, v represents the speed and direction at which the two points are moving towards or away from each other. This is important in calculating the damping force, which is the force that opposes the motion of the two points.

To break down the formula even further, let's look at each term individually. The first term, -stiff * distance(p1,p2), represents the spring force, which is directly proportional to the distance between the two points. This means that the farther apart the two points are, the stronger the force exerted by the spring will be. The stiffness (or spring constant) is a property of the spring and determines how much force is needed to stretch or compress it.

The second term, -damping * v, represents the damping force, which is directly proportional to the relative velocity between the two points. This means that the faster the two points are moving towards or away from each other, the stronger the damping force will be. Damping is a property of the medium in which the two points are moving and can be thought of as resistance to motion.

To calculate the position of the spring for the next iteration, you would need to use the equations of motion, specifically Newton's second law (F=ma) and the kinematic equations to determine