Equation of oscillating circle

In summary, the conversation is about finding the equation of the osculating circle and verifying the accuracy of the calculations involved. The speaker has already found the radius of curvature and is now seeking guidance on how to proceed further. They are also working on fixing a mistake they made earlier. The solution involves finding the normal vector and using it to determine the centre of the circle.
  • #1
sakkid95
6
0
http://gyazo.com/bc7f6da4d4c4aca300bb5efb2410fc8d.png


The problem, and my solution are in the image. I need help on finding the equation of the osculating circle, I found radius but I don't know where to go from there. Also if you could just check if my math seems correct that would help me too, but my main problem is how I find the eqn for the circle... thanks in advance
 
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  • #2
You made a mistake differentiating t3.
You have the radius of curvature; from the tangent you can find the normal vector.
 
  • #3
Yea I noticed the error, I'm working on fixing it now. Can you elaborate more on how to find the radius? I'm not very good at this stuff..
 
  • #4
sakkid95 said:
Yea I noticed the error, I'm working on fixing it now. Can you elaborate more on how to find the radius? I'm not very good at this stuff..

You said you had the radius. If so, all you need is a line the circle's centre must lie on. The normal to the curve is that line.
 

FAQ: Equation of oscillating circle

What is the equation of an oscillating circle?

The equation of an oscillating circle is x = cos(t) and y = sin(t), where t represents time and x and y represent the coordinates of the circle.

How is the equation of an oscillating circle different from a regular circle?

The equation of an oscillating circle includes the use of trigonometric functions (cosine and sine) to create a circular motion, while a regular circle is defined by the equation x^2 + y^2 = r^2.

What does the "oscillating" part in the equation represent?

The "oscillating" part in the equation, represented by the cosine and sine functions, represents the circular motion of the circle. As time increases, the values of x and y oscillate between -1 and 1, creating a circular path.

Can the equation of an oscillating circle be used to model real-life phenomena?

Yes, the equation of an oscillating circle can be used to model many real-life phenomena, such as the movement of a pendulum, the motion of a satellite in orbit, and the vibrations of a guitar string.

What are some applications of the equation of an oscillating circle in science and engineering?

The equation of an oscillating circle has a wide range of applications in science and engineering, including studying the behavior of waves, analyzing the motion of particles in a magnetic field, and designing oscillating systems such as springs and shock absorbers.

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