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OfflineTrancedShroom
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Yet another Calculus Problem
    #5797154 - 06/27/06 08:20 PM (17 years, 7 months ago)

Well first of all let me tell you I am pretty decent at Calculus, but like a human I can only get so many things right. I am a college student and I am taking this Calculus class as a summer school course, also I am doing this as a video course and doing on-line problems. I do not have a teacher at hand to help me with my questions and also the teacher does not make the homework up in-which they generally do. Also the videos are 3 years old and since then they have changed books and material.

So my question is can someone help me from the kindness of their heart so I am not scarred from this later on. I couldnt get any help from Nasbar because he said this is introductory Calc and I should know this. Well yes it is, but I am in this class with no teacher and problems that aren't covered by my teacher in the videos. I have all but the last question answered for this problem. PLease help me fellow Shroomerites.

An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically. The equation of motion is s = 2 cos(t) + 3 sin(t), t 0, where s is measured in centimeters and t in seconds. (We take the positive direction to be downward.)
(a) Find the velocity v at time t.
v(t) = -2sin(t)+ 3cos(t)
Find the acceleration a at time t.
a(t) = -2cos(t)- 3sin(t)

(b) Graph the velocity and acceleration functions.

(c) When does the mass pass through the equilibrium position for the first time?
s= 2.554

(d) How far from its equilibrium position does the mass travel?
cm =3.66

(e) When is the speed the greatest?
sec= ?

I would sure appreciate the help.


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Offlinerazorbladeshoes
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Re: Yet another Calculus Problem [Re: TrancedShroom]
    #5797227 - 06/27/06 08:42 PM (17 years, 7 months ago)

Quote:

TrancedShroom said:
(e) When is the speed the greatest?
sec= ?





One way to find the maximum or minimum for any function like velocity is to take the derivative and find the values for 't' where it's equal to 0. In other words, take the acceleration and figure out where it crosses the x-axis. Just to help you visualize: when the accelerations cross the x-axis (=0), the object has just finished accelerating one way and is about to start accelerating another way.

So your acceleration is: -2cos(t)- 3sin(t). That expression is equal to zero when t=2.554 and t=5.695, so those are locations where velocity COULD be a maximum, or COULD be a minumum. At t=2.554, the velocity is -3.606, so that's a minumum. At t=5.695, v=3.606, so that's a maximum.

All you need to remember is that maximums and minimums of a function occur where it's derivative is equal to zero.

Dave


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Invisiblekake
The answer to1984 is 1776.
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Re: Yet another Calculus Problem [Re: TrancedShroom]
    #5797236 - 06/27/06 08:46 PM (17 years, 7 months ago)

It's been a while since I've done any calculus.  I am going to try and think about this, but one thing to consider if you haven't already is that as a wave the speed will be the greatest when acceleration = 0 (this also signifies two other points - when the mass changes direction top-bottom)

Hope that helps :smile:


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The answer to 1984 is 1776.


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Invisiblekake
The answer to1984 is 1776.
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Re: Yet another Calculus Problem [Re: kake]
    #5797237 - 06/27/06 08:47 PM (17 years, 7 months ago)

Ahh, razorblade beat me to it, with a much more thorough explanation :smile:


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The answer to 1984 is 1776.


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OfflineNashbar
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Re: Yet another Calculus Problem [Re: kake]
    #5797243 - 06/27/06 08:50 PM (17 years, 7 months ago)

I was/am nowhere near sober enough to attmept that


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OfflineTrancedShroom
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Re: Yet another Calculus Problem [Re: Nashbar]
    #5797260 - 06/27/06 08:56 PM (17 years, 7 months ago)

WEll not to be an asshole Nashbar, but if it is Introductory Calculus and I am in that class, then I will have problems every now and then. And you said that this was easy stuff to do, but you just mentioned that you are too intoxicated to do this.

Like I said not being an asshole, just trying to put you in my shoes.

Thanx Razorbladeshoes.


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OfflineNashbar
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Re: Yet another Calculus Problem [Re: TrancedShroom]
    #5797263 - 06/27/06 08:58 PM (17 years, 7 months ago)

I was in your shoes. Looks like kake was too.


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OfflineTrancedShroom
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Re: Yet another Calculus Problem [Re: Nashbar]
    #5797278 - 06/27/06 09:03 PM (17 years, 7 months ago)

Yea well, my teacher is a CD and my homework is on computer with Symbolic Formating and is put on by a different person in-which the homework is now up to date and the videos aren't. It sucks, but I am the teacher and the student and most of the time so is my girlfriend the teacher which helps me out.


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OfflineNashbar
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Re: Yet another Calculus Problem [Re: TrancedShroom]
    #5797311 - 06/27/06 09:14 PM (17 years, 7 months ago)

you forgot to include my reference to Leibniz and Newton


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