Calculating Maximum Net Force in Simple Harmonic Motion

[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?

 

[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)?

 

[Dark Visitor]

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

 

[rock.freak667]

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

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

 

[Dark Visitor]

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

 

[rock.freak667]

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

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

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

 

[Dark Visitor]

So: a = dv/dt?

But how does that help me with this?

 

[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?

 

[Dark Visitor]

No I do not.

 

[rock.freak667]

No I do not.

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

 

[Dark Visitor]

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

 

[rock.freak667]

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

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


do you understand how to differentiate a function?

 

[Dark Visitor]

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

 

[rock.freak667]

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

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?

 

[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?

 

[rock.freak667]

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?

read about is http://www.intmath.com/Differentiation/Differentiation-intro.php"

 

[Dark Visitor]

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

 

[rock.freak667]

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?

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

read http://www.analyzemath.com/calculus/Differentiation/trigonometric.html" as well

 

[Dark Visitor]

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

 

[rock.freak667]

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

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)?

 

[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.

 

[rock.freak667]

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.

Because if you have x=Acos(ωt) and you want to find F_max=ma_max, chances are you will need 'a' to get 'a_max'

 

[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 a_max?

 

[rock.freak667]

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

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

 

[Dark Visitor]

Well, do I need to use the equation:

a(t) = -w²Acos(wt) ?

 

[rock.freak667]

Well, do I need to use the equation:

a(t) = -w²Acos(wt) ?

yes that is what you'd get had you differentiated x(t).

so now that you know a(t). At what value,cos(ωt) maximum?

 

[Dark Visitor]

In my notes, I have

a_max = w²a

Is that what you are going for?

 

[rock.freak667]

In my notes, I have

a_max = w²a

Is that what you are going for?

yes, but you did not follow the question template, so I really did not know what equations you had.

Had x been x=t⁵+e^tsin2t, you would need to differentiate.

 

[Dark Visitor]

Sorry about that. I found it buried in my notes, and when I posted this, I didn't think I would need that, so I didn't have my notes out.

So what do I do now?

 

[rock.freak667]

Sorry about that. I found it buried in my notes, and when I posted this, I didn't think I would need that, so I didn't have my notes out.

So what do I do now?

a_max=ω²A.

F_max=ma_max

I think you can get F_max from here