## FaisalAyaz 3 years ago 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.

1. MrMoose

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

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

3. FaisalAyaz

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

4. MrMoose

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

5. MrMoose

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

6. MrMoose

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

7. MrMoose

So, what is the maximum of a cosine function?

8. FaisalAyaz

1

9. MrMoose

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

10. FaisalAyaz

i think 12

11. MrMoose

yes

12. MrMoose

At what time does the speed become 12?

13. FaisalAyaz

don't know.may be 0

14. MrMoose

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

15. MrMoose

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

16. FaisalAyaz

which first equation?

17. MrMoose

the equation for position as a function of time

18. FaisalAyaz

f(t)=4sin(3t)

19. MrMoose

yes

20. FaisalAyaz

what i do with this now? please explain

21. FaisalAyaz

i put t=0 so position is zero?

22. MrMoose

Yes

23. FaisalAyaz

ok.Thanks a lot.

24. MrMoose

You are welcome