Asked by Madlyn Roberts

A weight is attached to an elastic spring that is suspended from a ceiling. If the weight s pulled 1 inch below its rest position and released its displacement in inches after t seconds is given by x(t)=(5pt+p/3. Find the first two times for which the displacement s 1.5 inches.

PLEASE HELP !
Answered by Reiny
looking back at your earlier attempts at typing this question I am going to guess you meant

x(t)= 2 cos (5πt+π/3)

you want this to be 1.5
2cos (5πt + π/3) = 1.5
cos (5πt + π/3) = 1.5/2 = 3/4
I know cos( .722734..) = 3/4
so 5πt + π/3 = .722734
5πt = -.3244633
t = -.020655975

now the period of 2cos(5πt + π/3) is 2π/(5π) = 2/5 or .4
so adding .4 to any answer will produce a new answer.
so t = -.20655.. + .4 = .379344
t = .379344 + .4 = .77934..

check:
let's take t = .77934...
x(t) = 2 cos(5π(.77934 + π/3)
= 2 cos 13.289..
= 1.5
YEAHHHHH
Answered by Madlyn Roberts
ouh maaann. thaaaans a buunnchhh :)
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