Questions tagged [spring]

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

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Dynamics of a bouncing capsule

I am working on a research project investigating the bounce of a capsule. I have tried to model it using conservation of energy, where we considered torque by normal force and friction during the ...
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273 views

Equilibrium points of three masses on a rigid spring ring with gravity

I'm trying to find the equilibrium points of a given system using Lagrangian mechanics (the system is still not rotating at the beginning). should I find the diagonal matrix for the characteristic ...
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2answers
42 views

What are the maximum spring lengths of a double spring pendulum?

NOT a duplicate of Maximum length stretch of vertical spring with a mass?, I am asking about a system with two connected springs, as shown in this diagram For a single spring, you can simply equate ...
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Equipartition and coupled harmonic oscillator system

This question has to do with analyzing how equipartition sets in for a system such as a coupled harmonic oscillator system. Take, for example, a system as shown in the figure: $\xi$ denoting the ...
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118 views

Deformation of an elastic ball

Suppose a free sponge ball is being compressed, due to applying a known force in a specific direction. The ball's shape will be distorted. Given are the direction of the applied force, as well as its ...
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1answer
892 views

How resistance in coils affects the damping of oscillations of a magnet through them

I performed an experiment where I connected a magnet to the end of a spring with the north side on the bottom. The magnet at the tip of the coil was aligned to pass through a column of coils of about ...
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256 views

Why is it that a coupled mass-spring system will always produce a diagonalizable matrix?

If you take a system like the one in the image, and you do the $y=x'$ trick to turn it into a first-order system of equations ($x_{1}$ or $x_{2}$ being the displacement of the mass $m_{1}$ or $m_{2}$ ...
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29 views

Why do different parts of a spring with mass stretch by different amounts?

If a massed spring is kept horizontal why should different parts stretch by different amounts? Suppose a one end is fixed, and the other is free with a velocity $v$ (uniform velocity) Suppose in $t$ ...
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1answer
57 views

Average energy of an SHM

Why do we usually calculate the average potential or kinetic energy of a simple harmonic motion with respect to time, why not with respect to position? Why even calculate average energy for an SHM? ...
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330 views

How do tension and linear density affect speed of waves in spring? (Qualitative)

Wave speed, tension and linear density (mass per unit length) can be related by the following equation: $$v=\sqrt{\frac{T}{\mu}}$$ The derivation of the equation could be done by using calculus. I ...
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3answers
86 views

Does a spring's $k$ affect the acceleration of a coupled mass?

Suppose I have a spring of spring constant $k$ attached to a mass $m$, with a constant force $F$ applied to the free end of the spring thus accelerating the mass. What happens to the acceleration of ...
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158 views

How to estimate the kinetic energy loss of a rigid cube after it colliding with a heavy spring at rest?

In an environment without gravity, there is an unfixed, motionless, uniform spring with non-negligible mass m, length L, and stiffness k suspending and a rigid cube with mass M moving with velocity v ...
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34 views

Springs Properties

I want to ask for a knowledge (preferably online) source about springs properties. I would like to know how Logarithmic decrement relates to type of material and spring shape (type) and how to ...
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485 views

Measuring Stiffness & Spring Damping Coefficient of Hard Rigid Material Objects

I have a set of objects made out of mostly stiff materials and what I want to do is to find out the stiffness and spring damping coefficients of those objects. I need to find out the values ...
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112 views

Spring constant and a spring's decompressed length

I wonder why the decompressed/free length of a spring doesn't change the spring constant $k$. I'll give the equation for $k$ here: $k = \frac{Gd^4}{8nD^3}$ For a fixed number of coils, if the free ...
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1answer
52 views

Reason for applying energy conservation and balancing force

I've this question When asked I was told that we will balance force for $2m$ object i.e., $(2\mu)2mg=Kx$ And we will conserve energy for $m$ mass i.e., $Fx=\frac{1}{2}kx^2+\mu mgx$ Both the blocks ...
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1answer
27 views

Can the Newton - Euler equations be used to model a rigid body attached on several springs?

imagine a three dimensional rigid body with known Moment of Inertia (at the center of mass) $I_{\text{cm}}$ which is suspended by several springs at different points on the surface of the body. The ...
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33 views

Elastic force expression

I would like to know how to properly write the elastic force in the classic x and y axes. I know that the global formula is $\vec{F_{el}}= -k\vec{x}$, but sometimes the situation is little bit ...
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2answers
66 views

Analysis of a spring-block motion when the point of suspension is accelerating vertically upward

I was taught to apply a "pseudo force", [which is equal to mass × acceleration (of point of suspension)] in the direction opposite to the point's acceleration and then proceed the way I ...
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1answer
112 views

Block attached to spring oscillating on a surface with friction

Consider a block of mass $m$ moving with initial velocity $v_o$ attached to a spring with spring constant $k$, on a terrain which has a coefficient of kinetic friction $\eta$ and coefficient of static ...
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37 views

What is the next higher order correction to Hooke's Law for a typical steel spring?

Near equilibrium the potential of a typical steel spring is well approximated by a quadratic function. I'm having trouble finding a reference for the what is the next-to-leading order contribution, ...
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1answer
49 views

Cohen-Tannoudji coupled harmonic oscillator

In the Cohen-Tannoudji QM book they say that the potential $$V(x)=\frac{1}{2}m\omega^2(x_1-a)^2 + \frac{1}{2}m\omega^2(x_2+a)^2 + \lambda m\omega^2(x_1-x_2)^2$$ describes two classical coupled ...
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2answers
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What does the work term mean when analyzing a ideal gas and spring system?

This problem has been bugging me for a long time now. It states that given an insulated cylinder which contains a spring and an ideal gas, you must calculate the work required to compress the gas, ...
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1answer
38 views

Modeling elastic tree branch (Double torsional pendulum?)

I’m trying to model “bending tree branch like motion” and it seems, that it can be described with some kind of «upward facing torsional pendulum” I guess. The construction is facing upward and start ...
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Mechanical energy conservation for different chosen systems

I studied work-energy theorem and the equation for mechanical energy conservation yesterday. I’m not able to understand how to identify forces when choosing a system (which force is which). This is ...
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290 views

Spring whose spring constant is a piecewise function of displacement—is this possible?

A bungee cord is essentially a very long rubber band that can stretch up to four times its unstretched length. However, its spring constant varies over its stretch [see Menz, P.G. “The Physics of ...
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Predict the behaviour of this system involving magnets oscillating on springs through connected coils

I came across an interesting problem recently and started to think about the situation in more detail. Here is the setup: Identical bar magnets are suspended from identical springs, with the North ...
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340 views

How does neglecting the mass of a spring with non-negligible mass affect the calculation of the total energy of the oscillator?

Consider a spring-mass system with spring constant $k$ undergoing simple harmonic motion with amplitude $A$. How/why will neglecting the mass contributed to the oscillator by the spring itself affect ...
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3answers
208 views

How would gravity affect a spring?

I'm currently in the process of writing a novel and I would like to add realism, I'm writing in a concept that involves springs stretching and tightening due to a constant fluctuating gravity. I'd ...
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280 views

A question about an assumption on a Very Basic Hooke's Law problem

A question states: A uniform beam AOB, O being the mid point of AB, mass $M$, rests on three identical vertical springs with stiffness constants $k_1$, $k_2$ and $k_3$ at A, O and B respectively. ...
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1answer
91 views

Help understanding a spring-mass system where mass is not attached

This is the scenario: We have a spring resting on a surface with no mass on it. Let the $y$ position of the top of the spring be $l_0$. When we put an object with some mass on top of the spring, the ...
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How to find the path of a cantilever beam's tip when it's bent?

I'm trying to analyze the harmonic motion of a hacksaw blade with one end fixed to the table. I'm trying to get an equation from Hooke's Law F = kx, but I'm not sure about how to calculate the ...
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5answers
532 views

Derivation of the work-energy theorem

We state the following version of work-energy theorem : $$ K_2-K_1=Fd=W $$ Where acceleration is assumed to be constant, so is the force $F$. Then the physicists proceed by writing $K_2-K_1=F[x(t_2)...
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Collision response with spring physics in RK4

I'm trying to figure out what's in the title. I've gotten regular spring physics working and now I'm trying to do something similar with actual collisions (player character colliding with the ground ...
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How can I calculate a spring's constant, using its characteristics?

I want to construct a device for a school project, so I need some springs of specific constants $k$. I found some companies that can construct the springs, but they need their dimensions. I want to ...
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109 views

Potential energy of and forces within a massive spring

So, I've been doing problems related to calculating the time period of SHM for a spring mass system where the mass is M, and the spring has a finite mass m. The standard method of dealing with this ...
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2answers
304 views

Is the equation of motion for a spring-damper system the same whether oriented upward or downward?

So every spring-damper system I've found online has the equation of motion: $$mx''+cx'+kx=0$$ I can understand how this is derived when downwards is positive, but what about when upwards is ...
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Physics of harmfull bungee jumping and hanging

According to the Wikipedia section on long drop hanging, the risk of decapitation increases with length of the rope. By analogy I expect that a long enough bungee rope can tear jumper's leg off. I ...
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Potential energy stored by an elastic circular loop on deformation to an ellipse

This question is related to an origami circular loop that I built. This structure is elastic and I intend to find the elastic potential energy stored by it when I deform it to an ellipse. My actual ...
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101 views

Find spring stiffness of a frame structure

I would like to calculate the spring constant of a frame structure. I thought that I could do it like this: I apply a point force on the structure: Then I calculate the displacement at that same ...
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507 views

Deduce transfer function in a mechanical network

I am familiar with a 2 degree-of-freedom (2DOF) system like it is depicted here: Assume all parameters are unknown. Now, how do I find the values of the parameters in case of A) a spring and ...
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Hanging mass from spring/ Setting potential to 0

I'm working a problem from Taylor's Classical Mechanics Book, and it's highlighted a couple issues I never quite wrapped my head around (despite getting good marks in advanced undergrad mechanics and ...
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612 views

Differential equation for an accelerometer

I am having troubles deriving the 2nd order differential equation for the system below, where $r=y-s$. According to my lecture notes the differential equation is $$ M\frac{d^2r}{dt^2}+b\frac{dr}{dt}+...
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83 views

Why can I assume the force to be constant in this particular interval?

If I have force, or any function $f(z)$, I was told that I can assume it to be constant only in the interval $dz$. However, in this case, I had to calculate the work done by the spring force as a ...
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1answer
82 views

Predicting the behaviour of a spring-mass system under the influence of regular periodic impulses

Here is the question: I have a mass 'm' connected by a spring to a wall. The setup is horizontal. The time period of the mass is 'T0' determined by the spring constant 'k'. The mass obeys a position ...
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270 views

Simplifying three mass, two springs system

I have a system of three equal masses connected by two equal string system. x_1 x_2 x_3 *--------*---------* ------> x M k M k M ...
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The force of a spring

I am new in continuum mechanics and I want to prove the formula which gives the force given by a spring : $$F_{max}= \frac{Ed^4(L-nd)}{16(1+\nu)(D-d)^3 n}$$ where : $E$ – Young's modulus $d$ – ...
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Torsion Spring Moment Calculation

I'm trying to extend the idea of a translational spring to a rotational spring. Consider a spring that acts on all displacements of a body: $$ \mathbf{F} = \begin{bmatrix} F_x \\ F_y \\ F_z \end{...
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2answers
103 views

Assume two springs with constant $c_1$ and $c_2$ are based in the following scenarios. Figure out the masses for equal displacement

Assume two springs with constant $c_1$ and $c_2$ are based in the following scenarios. Figure out the masses for equal displacement. More specifically I am to figure out what masses $m_1$, $m_2$ will ...
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75 views

What can take kinetic energy, transform it into potential energy when pressed on, and put back out as kinetic energy when released (besides a spring)?

A spring can only hold so much of the kinetic energy. For example, a 1 cm spring can hold less than 5 J. Is there anything that can hold a large amount of energy but be fairly small?