# Homework Help: Max. Net Force

1. Dec 6, 2009

### Dark Visitor

The position of a .64 kg mass undergoing simple harmonic motion is given by x(t) = (.16 m)cos($$\pi$$t/16). What is the maximum net force on the mass as it oscillates? (hints: First, match the quantities in the equation above to x(t) = Acos($$\omega$$t). Next, recall that the max. net force equals the product of the mass and the maximum acceleration.)

* 3.9 x 10-3 N
* 9.9 x 10-3 N
* 1.3 x 10-3 N
* 6.3 N

I don't really understand this problem and I need some help. So if anyone would be willing to help, I would really appreciate it. Where do I begin?

2. Dec 6, 2009

### rock.freak667

well you know F=ma.

You don't have an expression for a. You know $x(t)=0.16cos(\frac{\pi t}{16})$. Can you find a(t)?

3. Dec 6, 2009

### Dark Visitor

I don't understand how. Would it look anything like the x(t) one?

4. Dec 6, 2009

### rock.freak667

x is a displacement. Do you know how to get velocity from displacement?

5. Dec 6, 2009

### Dark Visitor

Not that I know of. Please explain it to me.

6. Dec 6, 2009

### rock.freak667

velocity is the rate of change of displacement: v= dx/dt

acceleration is the rate of change of velocity. Can you find acceleration now?

7. Dec 6, 2009

### Dark Visitor

So: a = dv/dt?

But how does that help me with this?

8. Dec 6, 2009

### denverdoc

Maybe try working on one of these problems at a time ;-D.

Acceleration and force will be maximal when a is at a maximum. Do you know how to do derivatives and do max/min problems?

9. Dec 6, 2009

### Dark Visitor

No I do not.

10. Dec 6, 2009

### rock.freak667

well find a(t). Now think, cosine and sine are maximum when they equal to what number?

11. Dec 6, 2009

### Dark Visitor

I still don't understand how to do that when we don't know x, t, or v.

12. Dec 6, 2009

### rock.freak667

$$x=0.16cos(\frac{\pi t}{16})$$

do you understand how to differentiate a function?

13. Dec 6, 2009

### Dark Visitor

No. How do I do that, and how does that help me with this (I mean where do I apply it)?

14. Dec 6, 2009

### rock.freak667

The entire problem relies on your knowledge of calculus. I must ask, if you do not know how to find the derivative of a function, how did you get this problem as homework?

15. Dec 6, 2009

### Dark Visitor

I don't know any calculus. I have only taken Algebra and Trig., and my teacher gave me these, so they must be using things I know, or should know. Any way you can explain that more in terms I can understand?

16. Dec 6, 2009

### rock.freak667

Last edited by a moderator: May 4, 2017
17. Dec 6, 2009

### Dark Visitor

Okay, I think I understand it a little better now. But where and how do I apply that to this problem?

18. Dec 6, 2009

### rock.freak667

Last edited by a moderator: May 4, 2017
19. Dec 6, 2009

### Dark Visitor

Okay, but I am still completely lost on this...

20. Dec 6, 2009

### rock.freak667

Read up on differentiation some more. But for this problem you need to know these

y=sinkx, dy/dx=kcoskx

y=coskx, dy/dx=-ksinkx.

With these can you find a(t) given x(t)?

21. Dec 6, 2009

### Dark Visitor

Well, reading the problem over, it says to match the quantities in the above equation, which leaves me with:

A = .160 m and $$\omega$$ = $$\pi$$/16

But I still don't understand where your differentiations come into play.

22. Dec 6, 2009

### rock.freak667

Because if you have x=Acos(ωt) and you want to find Fmax=mamax, chances are you will need 'a' to get 'amax'

23. Dec 6, 2009

### Dark Visitor

Okay, I see what you're saying. And it makes sense lol. But where do I go from here to get to a or amax?

24. Dec 6, 2009

### rock.freak667

Find 'a' and then you can get 'amax' from 'a'

25. Dec 6, 2009

### Dark Visitor

Well, do I need to use the equation:

a(t) = -w2Acos(wt) ???