FaisalAyaz Group Title A spring hanging from the ceiling vibrates up and down. it's vertical position at time (t) is given by f(t)=4 sin(3t). (a) Find the velocity of the spring at time t. (b) What is the spring's maximum speed. (c) what is location when it reaches its maximum speed. one year ago one year ago

1. MrMoose Group Title

You know that the position as a function of time is: $x(t) = 4\sin(3t)$ you also know that velocity is defined as: $\frac{dx}{dt}$

2. MrMoose Group Title

can you find the derivative of: $x(t) = 4\sin(3t)$

3. FaisalAyaz Group Title

Yes that is the ans of a.what about b and c parts?

4. MrMoose Group Title

so we want to find the maximum of: $12\cos(3t)$

5. MrMoose Group Title

So this basically comes down to finding where the cosine function has it's maximums

6. MrMoose Group Title

and then using the value for the maximum of a cosine in the equation

7. MrMoose Group Title

So, what is the maximum of a cosine function?

8. FaisalAyaz Group Title

1

9. MrMoose Group Title

yes, so the maximum value for the speed must be:

10. FaisalAyaz Group Title

i think 12

11. MrMoose Group Title

yes

12. MrMoose Group Title

At what time does the speed become 12?

13. FaisalAyaz Group Title

don't know.may be 0

14. MrMoose Group Title

Yes, because cos(x) = 1 when x = 0

15. MrMoose Group Title

Now that you know the time at which it reaches its maximum speed, you can plug that into the first equation

16. FaisalAyaz Group Title

which first equation?

17. MrMoose Group Title

the equation for position as a function of time

18. FaisalAyaz Group Title

f(t)=4sin(3t)

19. MrMoose Group Title

yes

20. FaisalAyaz Group Title

what i do with this now? please explain

21. FaisalAyaz Group Title

i put t=0 so position is zero?

22. MrMoose Group Title

Yes

23. FaisalAyaz Group Title

ok.Thanks a lot.

24. MrMoose Group Title

You are welcome