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Unformatted text preview: ,− 361 ⎞ྏ
⎜ྎ
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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.
 Winter '06
 McAdam
 Derivative, Differential Calculus

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