# 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 ...
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 ...
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 ...
88 views

### 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 ...
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 ...
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 ...
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 $m_{2}$ ...
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 $t$ ...
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? ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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, ...
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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### 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, ...
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 ...
61 views

### 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 ...
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 ...
61 views

### 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 ...
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 ...
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 ...
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. ...
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 ...
69 views

### 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 ...