## theEric 2 years ago Hi! I have to find the velocity as a function of displacement for some given force functions. Here is the question: Find the velocity $$\dot x$$ as a function of the displacement $$x$$ for a particle of mass $$m$$, which starts from rest at $$x=0$$, subject to the following force functions:

1. theEric

One moment!

2. theEric

(a) $$F_x=F_0+cx$$ (c) $$F_x=F_0\cos(cx)$$ If I see the general technique, I might be able to get it! Thanks!

3. Saeeddiscover

You can use this relation

4. Saeeddiscover

|dw:1379923967464:dw|

5. theEric

Ah, thank you very much Saeeddiscover!

6. Saeeddiscover

Hold on a moment!

7. theEric

Okay!

8. theEric

Does that work out? Is the $$x$$ in $$F_x=F_0+c\large x$$ a function of $$t$$?

9. Saeeddiscover

For the second one, you may consider this way as well: |dw:1379924739346:dw|

10. theEric

Thank you!

11. Saeeddiscover

Please wait a moment. I got a mistake!

12. theEric

Okay! If it's in that last part, I can't find it because I don't know that material yet!

13. Saeeddiscover

|dw:1379925139264:dw|

14. Saeeddiscover

|dw:1379925286166:dw|

15. theEric

That all makes sense, thank you! I'll try to apply those to my problems soon!

16. theEric

I think I need to head to bed, though...

17. theEric

Thanks again! :)

18. Saeeddiscover

Both 1 and 2 you are given simply can be solved using the last equation I gave you. It is true and works properly.

19. theEric

Great! I will use that, then! Have a good day!