Problem Set 06s

Find the coordinates of point at which the tangent is

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

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