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

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Deriving the formula for energy stored in a spring without using geometry (determining the area under a curve)?

Using Hooke's Law, we know that the force applied is proportional to the extension of the spring. Therefore by plotting a graph of force against extension, through the area under the curve we are able ...
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1answer
150 views

Newton's Third Law As Discussed in Den Hartog's Mechanics

A question, but some preliminaries in order to avoid answers involving concepts not yet introduced in the text I'm reading--Den Hartog's Mechanics. Near the very beginning of his book, Den Hartog ...
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0answers
69 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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0answers
140 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
104 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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2answers
13k 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
424 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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2answers
418 views

Max extension of spring mass system

While attempting problems of simple harmonic motion I came across this problem, which has gotten me confused. A fixed horizontal spring is stretched by a constant force $F$. I am required to obtain ...
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2answers
82 views

Why is the restoring force directly proportional to extension?

When deforming any spring the deforming force is always greater than the restoring force until equilibrium is reached. So, if a constant deforming force caused an extension in any spring the restoring ...
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2answers
70 views

Doubt on series springs [closed]

Here is a description of the motion of two springs in series. The premise is that the force on the two springs is the same. This is derived from the following reasoning: when I pull the mass with a ...
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2answers
834 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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2answers
83 views

Elastic potential energy and equilibrium position when mass changes in vertical mass-spring system

I'm a bit stuck with this situation: Suppose that an object $A$ with mass M=8 kg at 10 mt above the floor falls from rest tied to an 2 mt elastic rope, which does not exert any force since $A$ falls 2 ...
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1answer
220 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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3answers
47 views

Resonant Frequency of 2 mass spring system

So the question goes if I has a spring with spring constant $k$ and two masses attached to this spring (one on either side) what is the resonant frequency of the system in terms of $m$ and $k$? ...
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2answers
44 views

Is a spring shaped like a sine wave?

It's just a casual observation, so I wanted to check it: A regular spring, when not completely compressed, looks an awful lot like a sine wave. The idea of a circular shape stretched out in the third ...
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1answer
92 views

mass attached to spring rotates in a horizontal circle [closed]

So here is the question I have: A mass of 2kg rotates at 1m/s in a horizontal circle on a table at the end of a spring with an elastic constant of 50N/m. If the original length of the spring is 2 ...
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2answers
235 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
172 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
3k 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
1k 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
474 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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2answers
64 views

How is a mass, suspended vertically by two springs in parallel, kept stable? [closed]

Consider a mass suspended vertically from above by two springs in parallel with different spring constants. Wouldn't the tension be different in each spring? How is this system kept in equilibrium?
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1answer
43 views

Does the stretching of a spring depend on its rest length?

I don't understand if the stretching of a spring depends on its rest length besides its force constant $k$. I'll make an example to show my doubt. Consider a vertical spring and a mass $m$ ...
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1answer
124 views

two object connected by a spring : momentum/energy topic [closed]

Here is my question below: Question Two objects A and B, connected by a light elastic spring with elastic constant 5.0 N/m, are initially at rest. The mass A is 2.0 kg and the mass B is 1.0 kg. ...
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1answer
56 views

Distance between coils on a massive spring

I'm trying to calculate the separation between coils on a massive spring with no weights attached under different conditions. I will present my solution to the problem in the case of a uniform ...
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1answer
50 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
145 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
3k views

Final velocity of a spring [closed]

I need to calculate the velocity of an object when it is thrown by a spring; we have to calculate the velocity from $U=\frac 12 kx^2$. Now I know that $U=L=F\cdot S$ and $S=\frac{v_f^2-v_0^2}{2a}$. ...
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1answer
849 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
571 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
7k 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
98 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
356 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 ...
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1answer
62 views

Help with a bungee jumping question [closed]

Hi I have this question: Imagine that you have been given the job of desiging a new bungee jumping platform. Customers of mass 57.4 kg will step off a platform, attached to a rope of unstretched ...
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1answer
96 views

Oscillation of non-uniform plank on parallel springs

A plank of length $l$ and mass $m$ is placed on two parallel springs, each with spring constant $k$ and equidistant from the plank's horizontal center of gravity. When the plank is displaced from it's ...
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1answer
77 views

How does K (spring constant ) changes? [duplicate]

How the spring constant changes when a spring is cut into equl or rational halves? What is the relation with the original K?
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1answer
271 views

Two bodies connected by a spring

I came across of a problem. It is about two bodies with equal masses connected by a spring with the coefficient $k$ and the length of $l_0$. Suddenly, a constant force $F$ is applied to the first ...
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1answer
150 views

How to Determine Viscosity using Damped Oscillations? [closed]

How does one find out the viscosity of a fluid, using viscous damping of an oscillating spring? Any help would be greatly appreciated.
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1answer
47 views

Particle hitting particles attached with springs [closed]

In classical mechanics if you have a particle moving in two dimensions and it hits a particle at rest although that particle is attached to a spring that is in turn attached to a third particle. ...
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1answer
198 views

General solution of a mass spring system

This is the differential equation that describes small amplitude vertical oscillations of a mass $m$ that is hanging from a spring $$\frac{d^2x}{d t^{2}} + \frac{b}{m}\frac{dx}{dt} + \frac{k}{m} x = ...
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2answers
132 views

Calculating velocity based on applied force

If I have a block sitting on a spring, ignoring air resistance, with 45N of stored elastic energy in the spring, and the block weighs 500g, what would be the process for calculating its maximum ...
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1answer
73 views

Problem about a spring which oscillates due to a external force [closed]

A person holds a spring of stiffness $k= 80$ N/m by its extremity A; In the other end there is a mass of $0.5$ kg. The spring is initially at equilibrium, when the person starts to shake the ...
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3answers
506 views

On the definition of elastic restoring force in a spring

How is the elastic restoring force defined exactly for a spring? We know by Hooke's law that $$F_\text{restoring} = -kx$$ but what does $F_\text{restoring}$ really mean? I thought up till now that ...
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1answer
222 views

simple harmonic motion and center of mass

We choose a system to be a spring + a connected body. If we stretch the body and leave it, it will make a simple harmonic motion. The center of mass of this system is approximately the center of mass ...
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4answers
649 views

Spring stiffness calculation problems

I am trying to model a 1 DoF electromagnetic vibration sensor (geophone) analytically and with finite elements. A geophone consists of springs, a permanent magnet and coils. The coils are suspended ...
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1answer
257 views

How to determine angular frequency of this system?

I am self studying on harmonic motion and springs. One of the problems is: Two identical objects of mass m are placed at either end of a spring of spring constant k and the whole system is placed on a ...
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3answers
229 views

Tension of 2 massless springs joined together

A cable is formed by joining two massless springs with different spring constants. Spring A has constant k1. Spring B has constant k2. If mass M1 hangs from the cable, is the tension greater on ...
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1answer
310 views

How to find an effective spring constant of a quadratic potential

If a potential energy is given like $U(r)=A^3/r^2+2B^3r$, how do I find the effective spring constant using Taylor Expansion? I compared spring constant $k$ to be equal to second derivative of ...
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1answer
359 views

Natural frequency of spring-mass system

We can found on internet videos or articles about resonance. For this they for e.g. take a system of two spring and mass in between. When they set force frequency to close to natural frequency. But ...
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1answer
173 views

Where does elastic energy come from?

I vaguely remember reading that the elastic potential energy of a spring, $\frac{1}{2} k x^2$ comes from mass which is turned into energy according to the law $E=mc^2$. I also remember hearing that ...