GrizzlyChicken
The position of a mass on a spring (relative to equilibrium) at time t <= 0 is
x(t) = 2 cos((pi)t) where x is in centimeters and t is in seconds. Answer the ques-
tions. Include units!
(a) What is the initial position of the mass?
(b) What is the initial velocity of the mass?
(c) What is the initial acceleration of the mass?
(d) Does the mass initially move towards the wall or away from it?
(e) At what point does the mass rst turn around?
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goformit100
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post the question in physics section Not here @GrizzlyChicken
GrizzlyChicken
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its in my calc book, isn't this math?
nphuongsun93
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a) put t = 0 and solve for x
b) find x' and put t = 0 and solve for x'
c) find x'' and put y = 0 and solve for x''
nphuongsun93
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it's both physics and math lol
nphuongsun93
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*typo fix* sorry
c) find x'' and put t=0
GrizzlyChicken
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wait, its x(t)=2cos((pi)(t))
GrizzlyChicken
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sorry
nphuongsun93
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still~ same way of solving :P
GrizzlyChicken
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damn, theres another error, i'm gonna look it all over again, for some reason copy and pasting changed everything
GrizzlyChicken
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at time t is greater or equal to 0. its right now
GrizzlyChicken
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so if i put 0 for t, its 2cos(0)
nphuongsun93
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yup, that's the initial position
GrizzlyChicken
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is cos(0)=1?
nphuongsun93
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yes
GrizzlyChicken
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then for b) derivative of 2 is 0 so its all 0
GrizzlyChicken
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maybe
nphuongsun93
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no no, find the derivative of the function x
GrizzlyChicken
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so the derivative of 2cos(pi*0)?
GrizzlyChicken
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which uses the product rule (0)(cos...)+(2)(-sin(0))
GrizzlyChicken
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and sin(0)=0
GrizzlyChicken
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so the velocity is 0
nphuongsun93
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wops sorry i'm here
x = 2 cos (pi t)
x' = -2 pi sin (pi t)
nphuongsun93
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do you know how to derivative?
GrizzlyChicken
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yea, did you use the chain rule?
GrizzlyChicken
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is that why pi is with -2?
nphuongsun93
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no chain rule.
derivative of cos is -sin. pi 's brought out when derivative.
nphuongsun93
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|dw:1349943924669:dw|
nphuongsun93
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derivative again for the acceleration equation
GrizzlyChicken
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-2cos(pi*t)
GrizzlyChicken
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wait
GrizzlyChicken
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-2pi*cos(pi*t)
nphuongsun93
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almost correct, but now pi is brought one more time so it's
-2 pi^2 cos (pi t)
GrizzlyChicken
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ohhh
nphuongsun93
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x = 2 cos (pi t) x0 = 2
x' = v = -2 pi sin (pi t) v0 = 0
x'' = a = -2 pi^2 cos (pi t) a0 = -2pi^2
and idk how to do d and e
GrizzlyChicken
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does the mass move toward the wall because the acceleration is negative?
GrizzlyChicken
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oh, thats alright. you've helped me enough.Thanks!