The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 t
ID: 2881813 • Letter: T
Question
The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 t 8. I have answered all the parts except for D. Please help me with part d.
(a) When is the position function decreasing? (Round your answers to one decimal place. Enter your answer using interval notation.) (0.3, 2.8), (4.1, 5.3), (6.6, 8) Correct: Your answer is correct. I already answered this.
(b) During how many time intervals is the particle's acceleration positive? 4 Correct: Your answer is correct. I already answered this.
(c) At what time is the particle at the farthest distance away from its starting position in the negative direction? (Round your answer to one decimal place.) t = 5.3 Correct: Your answer is correct. I already answered this.
d. How far away is it from its original position? (Round your answer to the nearest integer.)
For part D I am not receiving the right answer. please help me with it. thank you.
Explanation / Answer
just put
t = 5.3 in f ( t )
f ( t ) = 2 cos(3t) + 3 sin(2t), 0 t 8
so f ( 5.3 ) = 2 cos ( 3 * 5 .3 ) + 3 sin ( 2 * 5.3 )
==> 2 cos ( 15.9 ) + 3 sin ( 10.6 )
==>2 * 0.9617413 + 3 * 0.183951
===> 1.9234826191 + 0.55185405183 ===> 2.49076894807
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