Theory Video 1

00:06:42
https://www.youtube.com/watch?v=PiQSjY7yoGI

摘要

TLDRThe video explains the theoretical component of linear oscillatory motion, focusing on Hooke's Law, which describes the relationship between the force applied to a spring and its extension. It details how the restoring force exerted by a spring is proportional to the displacement from its equilibrium position, represented by the equation F = -kY. The video also discusses the equilibrium of an object hanging from a spring, where the net force is zero, leading to the relationship k = mg/y. Additionally, it highlights the importance of understanding the linear and non-linear regions of the force-displacement graph for springs, emphasizing the need to use the slope for accurate analysis.

心得

  • 📏 Hooke's Law relates force and spring extension.
  • 🔄 The restoring force acts opposite to displacement.
  • ⚖️ At equilibrium, net force is zero.
  • 📊 The slope of the force-displacement graph indicates the spring constant.
  • 🔍 Non-Hookean regions do not follow Hooke's Law.
  • 🧮 Use free body diagrams to analyze forces.
  • 📈 Only consider the linear region for accurate analysis.

时间轴

  • 00:00:00 - 00:06:42

    In this video, the theoretical aspects of linear oscillatory motion are introduced, focusing on Hooke's Law, which describes the relationship between the force applied to a spring and its extension. Hooke's Law states that the restoring force exerted by a spring (F_s) is proportional to the displacement (Y) from its equilibrium position, expressed as F_s = -K*Y, where K is the spring constant. The negative sign indicates that the restoring force acts in the opposite direction of the displacement. The video also discusses the equilibrium of an object hanging from a spring, where the net force is zero, leading to the equation K = mg/Y. It emphasizes that the displacement is proportional to the mass added to the spring and the spring constant. The video concludes by mentioning the importance of understanding the linear relationship in Hooke's Law and the significance of using the slope of the graph to analyze the data accurately, particularly in distinguishing between the linear (Hookean) and non-linear (non-Hookean) regimes.

思维导图

视频问答

  • What is Hooke's Law?

    Hooke's Law states that the force exerted by a spring is proportional to its displacement from the equilibrium position, expressed as F = -kY.

  • What does the negative sign in Hooke's Law indicate?

    The negative sign indicates that the restoring force exerted by the spring acts in the opposite direction to the displacement.

  • How is the equilibrium position defined in the context of a spring?

    The equilibrium position is where the net force acting on the object is zero, meaning the spring force balances the weight of the object.

  • What is the relationship between mass and displacement in a spring system?

    The displacement of the spring is proportional to the mass added to it, as described by the equation k = mg/y.

  • What is the significance of the gradient in the force-displacement graph?

    The gradient of the graph represents the spring constant and helps identify the linear (Hookean) and non-linear (non-Hookean) regions.

  • What is a Hookean spring?

    A Hookean spring is one that obeys Hooke's Law, exhibiting a linear relationship between force and displacement.

  • What happens in the non-Hookean region of the graph?

    In the non-Hookean region, the relationship between force and displacement is not linear, meaning Hooke's Law does not apply.

  • How can you determine the spring constant from experimental data?

    You can determine the spring constant by calculating the slope of the linear portion of the force-displacement graph.

  • What is the role of free body diagrams in this context?

    Free body diagrams help visualize the forces acting on the object and establish relationships between them.

  • Why is it important to consider only the Hookean region in analysis?

    Considering only the Hookean region ensures accurate calculations and relationships based on Hooke's Law.

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  • 00:00:00
    okay hello everyone this is the
  • 00:00:03
    theoretical component of the prelab
  • 00:00:06
    video for the week nine lab which is
  • 00:00:08
    linear oscillatory motion and in this
  • 00:00:11
    video I'm going to be going over some of
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    the things that you should theoretically
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    know about the lab um however if you
  • 00:00:18
    don't know them I am now going to teach
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    them to you so there's no you know real
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    issue if you didn't get up to the
  • 00:00:25
    lectures in this yet or anything like
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    that so I'm going to cover the stuff for
  • 00:00:27
    you the first thing we need to cover is
  • 00:00:31
    something called hooks
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    law all righty now hooks law is
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    essentially the relationship between the
  • 00:00:39
    force applied to a spring and its
  • 00:00:41
    extension well actually more
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    technically hooks law tells us that the
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    spring a spring right let's say it has
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    an object on the end of it right if this
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    spring is normally coiled up at some
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    position which we'll call the
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    equilibrium position and then it's moved
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    to some new
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    position right let's let's call this
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    value zero and let's call this value y
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    right Y is the deviation from
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    equilibrium soor I'll move my head out
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    of the way there I am okay right so if
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    hooks law uh hooks law basically tells
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    us that the force that the spring is
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    going to attempt to restore Itself by by
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    the restoring force from the spring
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    which we call FS it's going to be equal
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    to minus K Y where Y and F are vectors
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    so what this is telling us is that the
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    restoring Force the spring exerts is
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    equal to the displacement from
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    equilibrium that's what Y is the
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    displacement from
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    equilibrium
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    times K which is the spring constant
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    sometimes called the stiffness
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    constant and F here is the force from
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    the spring right now this minus sign
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    here right this minus sign here is
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    telling us that when the spring
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    displaces in One Direction so in this
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    case it's displacing down the restoring
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    force is in the opposite direction so in
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    this case it's up that's what this minus
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    sign indicates that's why I have put the
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    little Vector hats on top of these two
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    right because otherwise without the
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    vector hats the minus sign is
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    meaningless right the minus sign is here
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    to tell us that the direction of Y and
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    the direction of f are opposites so
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    that's the first thing hooks law now
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    when we have an object hanging from a
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    spring so let's say this object was of
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    mass n right when let's say our object
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    is at equilibrium so let's say it's at
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    um equilibrium right now it's
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    been moved some deviation right some
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    deviation will say y right from the
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    equilibrium point and now let's say it's
  • 00:03:10
    at rest right if it's at rest then the
  • 00:03:12
    net force is equal to zero and if we
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    drew our free body diagram we'd say well
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    our our object here it has a weight
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    force acting down of mg and it has a
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    spring force acting up of Ky now I
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    haven't included the negative sign this
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    time because I am indicating the
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    direction using my arrows right so I'm
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    pointing up and I'm saying the force is
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    upwards KY as opposed to the negative mg
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    downwards so in this case we'd say well
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    if the sum of the forces equal zero then
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    KY = mg or k = mg over y right so the uh
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    which is which is force over
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    displacement uh if you're using Force
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    terms so that's hooks law for a very
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    simple spring and for part one that's
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    all you need to know is essentially when
  • 00:04:07
    you take a object and you add more mass
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    to it it's going to move down more and
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    the amount that it moves down should be
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    proportional to the
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    um it should be proportional to the
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    amount of mass and the spring constant
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    however you might notice
  • 00:04:27
    there that it's in it's in absolute
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    terms right it's not saying for every
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    change in mass you get a change in
  • 00:04:34
    displacement right what you're going to
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    have in your graph you're probably going
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    to have some sort of graph that looks
  • 00:04:41
    something like this where you might have
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    force on the x-axis and displacement on
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    the y- AIS and your data is going to fit
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    a line like this it's going to have and
  • 00:04:54
    I talk about this in the next video it's
  • 00:04:56
    going to have this period where we'll
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    call it non hook in and that's where it
  • 00:05:00
    doesn't make a straight
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    line and then it'll have this period
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    where it is hook in right this this
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    hooking period that's where it makes a
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    straight
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    line and you're going to take the
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    gradient of this right your gradient and
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    in this case the gradient is going to be
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    the rise over the run which is Delta y
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    over Delta F so you're going to have to
  • 00:05:23
    somehow go back to our equation here and
  • 00:05:27
    think how can I relate Delta y over
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    Delta F or maybe maybe it's just that
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    upside down who knows o mystery anyway
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    so that's the first thing you want to
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    know right is that hooks law tells us
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    that the um magnitude of the force
  • 00:05:45
    exerted by a spring is equal to some
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    constant times the displacement from
  • 00:05:48
    equilibrium and of course that you can
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    draw a free body diagram to do some sort
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    of relationship between that spring
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    force and the um other forces acting on
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    the object
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    of course also remember that this that
  • 00:06:02
    equation is only true of a hook and
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    spring and a hook and spring is a spring
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    that is hook and hook and spring is a
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    spring for which you get a straight line
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    displacement between these two so you
  • 00:06:12
    get a straight line graph between F and
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    Y and for the periods in which it's not
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    a straight line that's the non- hookin
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    regime this is why we use the gradient
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    right if you took actual values like you
  • 00:06:23
    know if you took some y value and some f
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    value you'd be
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    including these hook in values in your
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    analysis this is why we need to use the
  • 00:06:32
    slope because we only want to consider
  • 00:06:35
    this data we want to essentially
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    consider things as starting from here
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    right that's really what where we want
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    our data point to be
标签
  • Hooke's Law
  • linear oscillatory motion
  • spring constant
  • equilibrium position
  • restoring force
  • force-displacement graph
  • non-Hookean region
  • free body diagram
  • spring force
  • mass and displacement