Calculate the Frenet framing, curvature and torsion of the helix (a cos(t), a sin(t), bt)

Calculate the Frenet framing, curvature and torsion of the helix

(a cos(t), a sin(t), bt)

Expert Solution

Colby Messinger answered 2 years ago

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , ,...

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , , ) B. The unit normal vector N=N= ( , , ) C. The unit binormal vector B=B= ( , , ) D. The curvature κ=κ=

If u(t) = < sin(8t), cos(4t), t > and v(t) = < t, cos(4t), sin(8t) >,...

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If u(t) = < sin(5t), cos(5t), t > and v(t) = < t, cos(5t), sin(5t) >, use the formula below to find the given derivative. d/dt[ u(t) * v(t)] = u'(t) * v(t) + u(t)* v'(t) d/dt [ u(t) x v(t)] = ?

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Suppose r(t)=cos(πt)i+sin(πt)j+2tk represents the position of a particle on a helix, where z is the height...

Suppose r(t)=cos(πt)i+sin(πt)j+2tk represents the position of a particle on a helix, where z is the height of the particle. (a) What is t when the particle has height 8? (b) What is the velocity of the particle when its height is 8? (c) When the particle has height 8, it leaves the helix and moves along the tangent line at the constant velocity found in part (b). Find a vector parametric equation for the position of the particle (in terms...

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The plane curve represented by x(t) = t − sin(t), y(t) = 7 − cos(t), is a cycloid. (a) Find the slope of the tangent line to the cycloid for 0 < t < 2π. dy dx (b) Find an equation of the tangent line to the cycloid at t = π 3 (c) Find the length of the cycloid from t = 0 to t = π 2

The cycloid has parametric equations x = a(t + sin t), y = a(1 - cos...

The cycloid has parametric equations x = a(t + sin t), y = a(1 - cos t). Find the length of the arc from t = 0 to t = pi. [ Hint: 1 + cosA = 2 cos2 A/2 ]. and the arc length of a parametric

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