## GrizzlyChicken 3 years ago 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?

1. goformit100

post the question in physics section Not here @GrizzlyChicken

2. GrizzlyChicken

its in my calc book, isn't this math?

3. nphuongsun93

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''

4. nphuongsun93

it's both physics and math lol

5. nphuongsun93

*typo fix* sorry c) find x'' and put t=0

6. GrizzlyChicken

wait, its x(t)=2cos((pi)(t))

7. GrizzlyChicken

sorry

8. nphuongsun93

still~ same way of solving :P

9. GrizzlyChicken

damn, theres another error, i'm gonna look it all over again, for some reason copy and pasting changed everything

10. GrizzlyChicken

at time t is greater or equal to 0. its right now

11. GrizzlyChicken

so if i put 0 for t, its 2cos(0)

12. nphuongsun93

yup, that's the initial position

13. GrizzlyChicken

is cos(0)=1?

14. nphuongsun93

yes

15. GrizzlyChicken

then for b) derivative of 2 is 0 so its all 0

16. GrizzlyChicken

maybe

17. nphuongsun93

no no, find the derivative of the function x

18. GrizzlyChicken

so the derivative of 2cos(pi*0)?

19. GrizzlyChicken

which uses the product rule (0)(cos...)+(2)(-sin(0))

20. GrizzlyChicken

and sin(0)=0

21. GrizzlyChicken

so the velocity is 0

22. nphuongsun93

wops sorry i'm here x = 2 cos (pi t) x' = -2 pi sin (pi t)

23. nphuongsun93

do you know how to derivative?

24. GrizzlyChicken

yea, did you use the chain rule?

25. GrizzlyChicken

is that why pi is with -2?

26. nphuongsun93

no chain rule. derivative of cos is -sin. pi 's brought out when derivative.

27. nphuongsun93

|dw:1349943924669:dw|

28. nphuongsun93

derivative again for the acceleration equation

29. GrizzlyChicken

-2cos(pi*t)

30. GrizzlyChicken

wait

31. GrizzlyChicken

-2pi*cos(pi*t)

32. nphuongsun93

almost correct, but now pi is brought one more time so it's -2 pi^2 cos (pi t)

33. GrizzlyChicken

ohhh

34. nphuongsun93

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

35. GrizzlyChicken

does the mass move toward the wall because the acceleration is negative?

36. GrizzlyChicken

oh, thats alright. you've helped me enough.Thanks!