Find the coordinates of point at which the tangent is

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ,− 361 ⎞ྏ ⎜ྎ ⎟ྏ 12 ⎠ྏ ⎝ྎ 6 6. A mass on a spring vibrates vertically. Its equation of motion is y(t ) = 4 sin(2t ) , where t is in seconds and x is in centimeters. a. Find the velocity and acceleration at time t . Solution: Velocity = y' (t ) = 4 cos(2t ) ⋅ (2) = 8 cos(2t ) Acceleration = tan 6t lim t →0 sin 2 t sin 6t 1 sin 6t 1 1 = lim ⋅ = lim ⋅ ⋅ t →0 cos 6 t sin 2 t t →0 1 cos 6t sin 2t sin 6t 1 t 6 sin 6t 1 2t = lim ⋅ ⋅ = lim ⋅ ⋅ t →0 t →0 t cos 6t sin 2t 6t cos 6t 2 sin 2t # 6 sin 6t & #1& # 1 2t & = lim % ( ⋅ ltim % ( ⋅ lim % ( t →0 $ →0 $ cos 6 t ' t →0 $ 2 sin 2 t ' 6t ' 1 = 6(1) ⋅ 1 ⋅ ⋅ 1 2 tan 6t lim =3 t →0 sin 2 t y'...
View Full Document

This document was uploaded on 02/27/2014 for the course M 408c at University of Texas at Austin.

Ask a homework question - tutors are online