An object such as a metal coil or air-filled tube which provides a force opposing the direction of deformation.

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Dropping a weight onto a spring scale

Say I drop a 5kg weight from a height of 1 meters onto a spring scale like many people have in their bathrooms. On impact the scale will show a higher weight than 5kg. Question: Which quantities ...
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2answers
1k views

Why does the acceleration $g$ due to gravity not affect the period of a vertically mounted spring?

For a vertically mounted spring, I was looking at the formula $ T= 2\pi \sqrt{m/k}$ for a period. Why doesn't the gravitational acceleration $g$ factor in?
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1answer
432 views

What is the two dimensional equivalent of a spring?

I'm trying to model isotropic linear elastic deformation in two dimensions. In one dimension, I know that a linear elastic material can be thought of as a spring which obeys Hooke's law $F=-k\Delta ...
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2answers
245 views

Bungee jumping - find spring constant

A person of mass $m$ is attached to a spring that its loose length is $l_0$. He is standing on a bridge and jumps off it, so he travels down a distance $2 l_0$ when measured from the bridge up to the ...
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1answer
2k views

How do I account for the direction of friction acting on a spring?

I would like to set up the equations of motion for a simple spring oscillator. Let's have a spring lying horizontally; we attach a small mass $m$ to the (massless) spring. The force of the spring ...
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1answer
237 views

Does a slinky hanging downward double in length if gravity doubles?

Also would a spring under tension greater than the force of gravity pulling the spring downward shrink in both directions until it has depleted it's stored energy while in free fall?
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1answer
59 views

Damping a spring force

I'm modelling particles in a system using a spring and damper force. $$F= kx -cv$$ $x=x_i -x_f$, where $x_i$=centre of spring and $x_f$= displaced position. Above $x$ is the displacement and $v$ is ...
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3answers
3k views

Where does the loss in gravitational energy of the load go when a spring is pulled?

A mass spring system is in equilibrium. If I pull on the load by $x$ meters, the energy stored in the spring is (this is what is given in my book): $$E=\frac12kx^2 $$ However, doesn't the load lose ...
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1answer
138 views

Equation of motion for system of springs

I need to find the equations of motion for the following system. If $x_1$ is $m_1$'s extension and $x_2$ is $m_2$'s, then, I feel like for $m_1$ we just need to consider $x_1$ giving $$m_1 a_1 = ...
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3answers
564 views

Why doesn't Lenz's law predict the behavior of a rod on springs in a magnetic field?

This comes from one of the free response questions from the AP Physics B 2014 exam. 5. (15 points) A conducting rod of mass $m$ and length $L$ hangs at rest from two identical conducting ...
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2answers
332 views

Stick and slip motion: mass and spring inside a box model

I am trying to determine a set of differential equation which can describe the motion of a mechanical system as below. Here, at the bottom we have a plate, and a box on top of it. Inside the box, ...
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4answers
140 views

The motion of a spring

I have a question about the force set by this spring, I saw many times that $\overrightarrow{F}=-Kx\overrightarrow{i}$. I'm asking why not using $\overrightarrow{F}=Kx\overrightarrow{i}$ without the ...
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1answer
259 views

rate of change of spring potential energy $\frac{dU}{dt}$

Suppose we have a setup like this. In orange are two wooden sticks sort of things, and they are attached to the block of mass $m$(as usual) at a joint which is hinge type something. A similar ...
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3answers
2k views

Spring-mass system with two springs and three masses [closed]

I'm trying to solve a system of springs and masses that is confusing me. First, the balls are all lined up linearly. Secondly, the ball in the middle has a smaller mass $m$ while the first and last ...
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2answers
541 views

Why do joined massless springs, act like a rope under tension?

In an oscillations exercise there is a spring attached to another spring, attached to a block. Long story short: I have to find the global $k$. In the solutions it says: "Because the springs are ...
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1answer
165 views

Could someone explain to me why this is sometimes right and sometimes not?

I do not remember when, but a while a ago I was told that for a spring with stiffness $k$ and a mass $m$, the equation $-kx = ma$ never holds. (assume a horizontal spring) So if I was given a problem ...
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2answers
290 views

In continuum mechanics, what is work potential in the context of total potential energy?

I'm reading a book on the finite element method. Specifically I'm looking at the background material where they are discussing potential energy, equilibrium, and the Rayleigh–Ritz method. The book ...
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1answer
824 views

Using Fourier Transforms to Solve Systems with springs of high frequency

I'm trying to numerically solve the differential equations of motion in a system with multiple springs of very high frequency. Because the solution is often a combination of rapidly-oscillating sine ...
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1answer
315 views

Lagrangian, Kinetic & Potential energy with two masses connected to three springs

Two masses $m_1$ and $m_2$ are on a frictionless surface. They are connected by three springs with constants $k_1,k_2,k_3$. $k_1$ and $k_3$ are attached to walls and $k_2$ is between the masses. $k_1$ ...
2
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1answer
230 views

Frequency of Oscillations about Circular Orbit [closed]

I'm trying to figure out the frequency of small oscillations about the basic circular path of a mass at the end of a spring, being spun around a table. I understand that the spring will stretch out a ...
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1answer
134 views

Extension of an unfixed spring

Suppose a spring with spring constant 1 N m^-1 is held horizontally. If a pull of 1 N is applied to its left end and a pull of 2 N is applied to its right end, how much longer would the spring be as ...
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1answer
128 views

Do I need to take elastic potential energy into account? [closed]

Let's say I have a vertical spring with end points $A$ and $B$ and length $a$ and a mass attached to the endpoint $B$. The mass is dropped from the point $A$ and I need to find the kinetic ...
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1answer
234 views

What forces are exerted on a clothespin in space?

Let's say a clothespin is modeled as a simple torsion spring as follows. Given: $p_1,\ p_2,\ p_3$: point-like objects of equal mass in 2-D space. All objects float in space, i.e. the center of mass ...
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2answers
532 views

Rotating spring system: Is my intuition correct?

Consider a solid spherical object of uniform density that is rotating on an axis A1. Perpendicular to that axis one can draw another line that passes through the sphere. On this axis, on both sides of ...
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1answer
256 views

How do determine the equation of motion of slinky?

I'm trying to analyze the forces exerted to slinky. First, I've divided both ends. The red vector is the force exerted by slinky itself, and the green vector is gravitational force. Force exerted ...
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1answer
491 views

Simple harmonic oscillator system and changes in its total energy

Suppose I have a body of mass $M$ connected to a spring (which is connected to a vertical wall) with a stiffness coefficient of $k$ on some frictionless surface. The body oscillates from point $C$ to ...
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0answers
52 views

Two solutions, A+ and A-, for masses connected via springs

My prof gives an example of trying to solve the equations of motion for a series of gliders each connected by springs, with the same spring constant. From looking at the $j-1$ through $j+1$ glider, he ...
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1answer
96 views

2D square lattice, nearest neighbor and next-nearest connected by springs

For my field theory class I am trying to build the Lagrangian for the following system. Consider a 2D square lattice where the nearest and next-nearest neighbor interactions are modeled by springs ...
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1answer
166 views

Imposing symmetries on asymmetrical dynamic systems

Let us say we have a one dimensional system of masses connected by springs. All the masses are equal and the springs alternate with spring constants of $k$ and $6k$. The appropriate way to analyze ...
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0answers
67 views

Question about massive spring and SHM [closed]

A mass $M$ is resting on the end of a spring with constant $K$. The mass of the spring is $m$, and the displacement of each element of the spring is proportional to the distance from the fixed end ...
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0answers
85 views

Can I use the reduced mass principle in a spring-damper system?

http://hyperphysics.phy-astr.gsu.edu/hbase/orbv.html#rm I want to know, if I can use the reduced mass principle to solve a two object spring-damper system. In the books and webpages that I have ...
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1answer
662 views

Spring system - 3 DoF system and its properties while changing stiffness

I was given the attached 3 degree of freedom spring system with the purpose of analyzing it. I came up with the following equation of motion and then I ran Matlab to calculate the corresponding ...
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2answers
8k views

How to find the compression of a spring attached to an object [closed]

I am having some trouble figuring out the equation needed to solve this problem. A 3.0-kg block slides along a frictionless tabletop at 8.0 m/s toward a second block (at rest) of mass 4.5 kg. A ...
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0answers
367 views

include the stretch of the spring own weight in potential energy for spring pendulum?

we are given a problem with spring with its own mass $m$. I am confused how to set up the PE term in the Lagrangian. Assume the spring has length of $L_{0}$ when it is laying on a table horizontally. ...
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3answers
1k views

where did I lose the negative sign when spring is in compression in a mass-spring problem?

Most books just tells you that spring force is $-kx$ since it opposes motion and to just write $mx''=-kx$ regardless if the spring is in tension of compression. But when I try to derive this using ...
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2answers
666 views

How could this damped oscillator ever go to infinity? Or negative infinity for that matter?

This is an ODE problem,but I cannot visualize why it can go to infinity or negative infinity. Consider $$x'' -6x' + 8x = 0$$ Where $x''$ is acceleration, $-6x'$ is the ...
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1answer
212 views

Spring oscillations and waves

Consider a block of mass $m$ attached to a spring. Let it oscillate at a frequency $f$. Now each part of the spring is in SHM. so this means a wave is propagating through this spring.bCan this wave be ...
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2answers
101 views

Hooke's Law and Simple Harmonic Motion

Can anyone explain how the following formula is derived and what it means? $$x'' = -n^2x $$ I was reading through my high school physics textbook and I stumbled upon a section on Hooke's Law. It says ...
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1answer
46 views

Variation in spring constant with respect to the length and no. of coils

Do the spring constant depend upon the length of the spring? No. of coils? Like what happens to the spring constant if you cut it in the half?
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1answer
1k views

Kinetic energy and potential energy variation over distance in SHM

When you compute the average potential energy of a horizontal spring mass system from the mean position to the positive amplitude A, the value comes out to be $\frac{1}{6}kA^2$. For the average ...
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1answer
2k views

Confused about relating spring force to maximum distance

I keep working through this problem and getting the wrong answer: A spring with spring constant k is positioned vertically and then compressed from its equilibrium length by a distance Δy. A ...
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2answers
939 views

Energy stored in a clothespin spring (non linear spring)

I was wondering how one would go about figuring out the energy stored in a spring in a clothespin. When opened the spring is deformed, but I don't have any intuition for why it gets stronger with ...
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2answers
338 views

Why is the spring constant $W_p''(0)$?

According to my physics book, the spring constant can be calculated from knowing the potential energy, with the formula $k = W_p''(0)$. I don't really understand why, and the book doesn't explain it ...
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1answer
23 views

Extension spring and permanent damage

Is there a way to calculate how far an extension spring can be extended before it suffers permanent damage? There are some online calculators, but how are they done? This calculator is the most ...
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1answer
67 views

Equation for calculating spring costant

I'd like to design some of my own springs in order to obtain some very specific forces for a project. There are plenty of guides on how to make an arbitrary spring, but none I've read explain how to ...
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1answer
481 views

Using gravitational potential energy and elastic potential energy in a problem?

This is a problem my professor worked on in class: The first thing he said was that we would use position 2 as the "reference height" and I'm not sure what that means exactly. He goes on to say ...
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1answer
312 views

Coupled Spring System (3 mass 3 springs)

Hello I am having trouble trying to find the correct model for this coupled spring system. The scenario is the following we have: Ceiling - Spring - Mass(1) - Spring(2) - Mass(2) - Spring (3) - ...
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2answers
4k views

Finding max height of a mass launched by a spring?

I have the following problem on my homework. The actual problem has numbers, but I figure using symbolic notation will help me understand the concept in the long run. A block of mass $M$ is launched ...
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1answer
90 views

Spring with changing equilibrium

Suppose that we have two cars on a track, each with a different mass. Now suppose that the cars are connected with a spring. We smack one car. I would like to write down the equations of motion for ...
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1answer
281 views

Modeling linear spring deformation in time

Suppose I had a spring (at equilibrium) and applied a certain force $F$, causing it to undergo elastic deformation. I know that by applying this specific force, hooke's law tells me that the spring ...