# Math Help - Curvature (2nd)

1. ## Curvature (2nd)

Find the curvature at the following point and then sketch this curve.

r(t) = <cos(2t), 2*sin(2t), 4t>, t = 0, t = Pi/2

Note: r is a vector

2. Hello, Ideasman!

If you have the formula for curvature, go for it!

This is a very unpleasant problem (especially without LaTeX)
. . I'll start it off for you.

Find the curvature at the following point and then sketch this curve.

. . r(t) .= .< cos(2t), 2·sin(2t), 4t >, . at t = 0, t = π/2

. . . . . . . . . . . . . . . . . . .| v x a |
Curvature Formula: . k .= .----------
. . . . . . . . . . . . . . . . . . . . |v|³

Given: .r(t) .= .< cos(2t), 2·sin(2t), 4t >

Then: .v(t) .= .< -2·sin(2t), 4·cos(2t), 4 >

Then: .a(t) .= .< -4·cos(2t), -8·sin(2t), 0 >

We will need:

Code:
              |     i            j         k |
| v x a |  =  | -2·sin(2t)    4·cos(2t)    4 |
| -4·cos(2t)   -8·sin(2t)    0 |

We also need |v|³ ._________________________
. . . where |v| .= .√4·sin²(2t) + 16·cos²(2t) + 16