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Help! Force of a Spring for Small displacements

  1. Mar 15, 2009 #1
    Help! Force of a Spring for "Small" displacements

    1. The problem statement, all variables and given/known data

    Okay, here is the diagram, untitled.jpg


    For "small horizontal displacements" of the mass:

    For the force exerted by each spring (TOTAL, not resolved) they are using:

    Fsp=kxcos(45) and then resolving it onto the x-axis they use

    Fsp x=kxcos25*cos45

    I do not understanding this at all.

    Why is the unresolved force using cos*45 ?

    I am thinking it has to do with the fact that we are assuming that we are making
    only "small horizontal displacements" of the mass.
     
  2. jcsd
  3. Mar 15, 2009 #2

    gabbagabbahey

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    Re: Help! Force of a Spring for "Small" displacements

    The key word is horizontal as-in 'along the x-axis'. The springs exert a force in response to displacements along their lengths. What component of the horizontal displacement points along the length of each spring?
     
  4. Mar 15, 2009 #3
    Re: Help! Force of a Spring for "Small" displacements

    Well, apparently x*cos(45)...

    But I have drawn it out like 4 times and cannot seem to see it. Guess you cannot really help me with that part though.
     
  5. Mar 15, 2009 #4

    gabbagabbahey

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    Re: Help! Force of a Spring for "Small" displacements

    Well, let's look at the spring in the first quadrant: the angle between the horizontal displacement (call the displacement [itex]\dec{d}=x\hat{i}[/itex]), and the unit vector along th length of the spring (call it [itex]\hat{n}[/itex]) is 45 deg. To get the component of d along n you take the dot product of the two vectors, and [itex]\vec{d}\cdot\hat{n}=||\vec{d}||*||\hat{n}||\cos(45)=(x)*(1)\cos(45)[/itex]

    Alternatively you can just use trig:

    http://img19.imageshack.us/img19/1719/springa.th.jpg [Broken]
     
    Last edited by a moderator: May 4, 2017
  6. Mar 16, 2009 #5
    Re: Help! Force of a Spring for "Small" displacements

    Yes, I was using the wrong triangle like the jerk that I am. Thank you for that G... That offers a lot of insight into my problem-solving strategies.

    Thanks again for your time,
    Casey
     
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