What is Springs: Definition and 676 Discussions

Hot Springs is a resort city in the state of Arkansas and the county seat of Garland County. The city is located in the Ouachita Mountains among the U.S. Interior Highlands, and is set among several natural hot springs for which the city is named. As of the 2010 United States Census, the city had a population of 35,193. In 2019 the estimated population was 38,797.The center of Hot Springs is the oldest federal reserve in the United States, today preserved as Hot Springs National Park. The hot spring water has been popularly believed for centuries to possess healing properties, and was a subject of legend among several Native American tribes. Following federal protection in 1832, the city developed into a successful spa town. Incorporated January 10, 1851, the city has been home to Major League Baseball spring training, illegal gambling, speakeasies and gangsters such as Al Capone, horse racing at Oaklawn Park, the Army and Navy Hospital, and 42nd President Bill Clinton. One of the largest Pentecostal denominations in the United States, the Assemblies of God, traces its beginnings to Hot Springs.
Today, much of Hot Springs's history is preserved by various government entities. Hot Springs National Park is maintained by the National Park Service, including Bathhouse Row, which preserves the eight historic bathhouse buildings and gardens along Central Avenue. Downtown Hot Springs is preserved as the Central Avenue Historic District, listed on the National Register of Historic Places. The city also contains dozens of historic hotels and motor courts, built during the Great Depression in the Art Deco style. Due to the popularity of the thermal waters, Hot Springs benefited from rapid growth during a period when many cities saw a sharp decline in building; much like Miami's art deco districts. As a result, Hot Springs's architecture is a key part of the city's blend of cultures, including a reputation as a tourist town and a Southern city. Also a destination for the arts, Hot Springs features the Hot Springs Music Festival, Hot Springs Documentary Film Festival, and the Valley of the Vapors Independent Music Festival annually.

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  1. W

    Is the derivative in my textbook correct here?

    Homework Statement Homework Equations d/dx The Attempt at a Solution d/dx (T) = d/dx(1/2mx'2) = mx'' d/dx(U) = d/dx(1/2kx2) = kx' ≠ kx It's probably me who made an error because I know that that equation (2.3) is the one I should be getting, but I don't understand how they did it because...
  2. L

    In dynamics, do we assume springs always resist motion?

    I'm making a vibration rig that represents a classic 2 mass, 3 spring system (See attached Image). (To clarify the image - there will be no forcing frequency. m=m1=m2 and k=k1=k2=k3) I'm using extension springs in the vibration rig. I plan to displace them in extension at an equilibrium point...
  3. X

    Coupled oscillator: 2 masses and 3 different springs

    Homework Statement Two harmonic oscillators A and B , of mass m and spring constants kA and kB are coupled together by a spring of spring constant kC .Find the normal frequencies ω' and ω'' and describe the normal modes of oscillation if (k C)2= kAkB) Homework EquationsThe Attempt at a...
  4. R

    Maximum speed of a cylinder dropped on a spring

    Homework Statement Cylinder A (mass = 5kg) is released from rest at a height h =100mm above a spring of stiffness k = 1.8 kN/m. Determine, (i) the maximum compression of the spring, (ii) the spring deflection when the cylinder’s velocity is a maximum, and, (iii) the maximum velocity of the...
  5. Tazerfish

    Length-adjustable gas springs

    I was uncertain wether to put this in the general physics forum, but I decided against it. How do length adjustable gas springs(like for example in office chairs)work ? I know how gas springs work and i even have an idea how length adjustable ones could work. Since you hear a "gas flowing...
  6. K

    Spring System in a Tower: Analysis and Calculations

    Homework Statement [/B] In a tower a princess throws a ladder of 20 plates of thickness d and mass m each, which are connected with springs of constant k and loose length l0. the window is at height H. 1) What's the elongation of each of the spring pairs? 2) What's the total ladder's length. 3)...
  7. K

    Cart with 2 springs and a sliding mass

    Homework Statement [/B] A cart of mass m is adjacent to a wall. it has a mass, also m, attached at point A to a loose spring of constant k. an identical spring is on the opposite wall. the floor of the cart is frictionless apart of the middle part CD with equivalent μ. a force F is applied to...
  8. P

    Mass and two springs in series: How to solve acceleration

    Hello! I have rather simple problem, but I can't find somehow answer for it: There are two springs in series, let's say spring 1 and spring 2. Springs are attached and spring 2 is attached to ground. In the beginning springs are not stretched. Let's say springs have spring constants k1 and k2...
  9. V

    Stable equilibrium of a 4 mass, 6 spring system

    Homework Statement I am making a physics engine for my computer science class and couldn't figure out how to get the spring/mass system to come to equilibrium into a box-like shape such as the one on the left. I can understand why the one on the right is in equilibrium but I don't know how to...
  10. ramialsaiad

    Derive the kinetic energy of a mass on two springs

    Homework Statement Hi I want to derive the equation of kinetic energy for a mass on two springs .. Here is the figure of the system: http://faculty.ndhu.edu.tw/~clcheng/class-98/gen-phy98/gen-phy98-1-Q2s.pdf Am I doing right for calculating the kinetic energy for the mass on two springs ...
  11. RicardoMP

    Normal Modes and Normal Frequencies

    Homework Statement I have to determine the frequencies of the normal modes of oscillation for the system I've uploaded.Homework Equations [/B] I determined the following differential equations for the coupled system: \ddot{x_A}+2(\omega_0^2+\tilde{\omega_0}^2)x_A-\omega_0^2x_B = 0...
  12. E

    Undetermined beam problem supported by three different springs

    Hi, I thought it would be an easy one but it isn't... I am trying to solve the problem of a beam supported by three different springs with a uniform distributed load:
  13. Z

    Finding mass of an object on a spring, given Frequency

    Homework Statement A mass m at the end of a spring oscillates with a frequency of 0.84 Hz . When an additional 730 g mass is added to m, the frequency is 0.65 Hz . Homework Equations f*2pi = w w = (k/m)^1/2 f = (1/2pi)*(k/m)^1/2 The Attempt at a Solution I simply used the third equation...
  14. K

    Finding Equilibrium and Motion of a Mass Connected to Two Springs

    Homework Statement the two springs are identical and have the same constant k. they also have the same contracted length l0. a force of ##k\cdot l_0## has to be applied in order to start stretching the springs from length l0 and on. L>l0, ##mg>k\cdot l_0##. The ring slides frictionless on the...
  15. Blockade

    Can someone explain to me the work equation for springs?

    I need to find the work done with springs but I don't understand this equation too well, can someone help me know what are each variable and how to find each of them? WH - fF*d = ΔK + ΔUs + ΔUg? I know that "WH" is the work done by the hand and that "fF*d" is force of friction * displacement...
  16. O

    Analyzing a Compressed Spring System

    It's not a homework/coursework question but I did get the system from my textbook. http://puu.sh/o03h7/32cdf7cffb.jpg I solved the question by analyzing the system at different stages. Initially both objects are moving with a velocity and having some mass so their kinetic energies are the...
  17. J

    Distorting force vs restoring force in springs?

    Awhile back, I was learning about springs, and restoring/distorting force. We even did an experiment where we hung a spring and put weights on it and pulling it down, watching it oscillate. From this, I assumed the distorting force was the force that stretched the spring and restoring force is...
  18. heartshapedbox

    Determining equilibrium position between two springs

    Homework Statement see attachment ***indicates correct answer Homework Equations F=ks The Attempt at a Solution I do not understand how this works, and I haven't been able to find any examples of this.
  19. J

    Springs in Series & Parallel

    Homework Statement Use data from your experiment to support the idea that Young's Modulus relates the material and is independent of shape and geometry whilst the spring constant is a function of the shape and geometry. The experiment involved stretching identicle springs (starting off with one...
  20. E

    Why is the ratio of displacements in springs different than expected?

    Homework Statement A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k, respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction...
  21. R

    What are the key factors to consider when using springs for cushioning a fall?

    Lets say there is a rigid metal box. It is 1meter wide, 2meters long and an undetermined height. The thickness of the box's metal walls are also undetermined. The entire box weighs 2 metric tons. There is a person lying face down or face up in this box, and inside the box, the bottom and top of...
  22. A

    Why are stiff springs more responsive?

    I know that stiff springs are more responsive than softer but why? It seems natural that this would be the case but what is happening during turn in? I read on another forum that the softer springs would store more energy than the stiff because they compress further. However two springs of...
  23. kostoglotov

    Damped vs Undamped Driven Springs and superposition?

    Modeling driven undamped spring systems in my diff eqs text at the moment. So I've just worked through the derivation of x(t) = C\cos{(\omega_0t - \alpha)} + \frac{F_0/m}{\omega_0^2-\omega^2}\cos{\omega t} And it's clear that this describes the superposition of two different oscillations...
  24. S

    What variables affect the amplitude and equilibrium of waves and springs?

    What variables are maximum at amplitude and equilibrium? What variables are minimum at amplitude and equilibrium? I'm confused about this topic... I know KE is max at equilibrium and PE is max at amplitude.
  25. Lito

    Harmonic motion- Two springs, One mass

    Homework Statement Two springs each have spring constant k and equilibrium length ℓ. They are both stretched a distance ℓ and then attached to a mass m and two walls (which are 4 ℓ apart). At a given instant, the right spring constant is somehow magically changed to 3k (the relaxed length...
  26. Utilite

    Springs and Hooke's Law -- Unequal forces applied to the two ends....

    Okay here is my question. Assume that you are pulling a spring with 3N from one end and 5N from the other one. How can we apply Hooke's Law in this case? And let's assume that the spring isn't stretching anymore just to simplify things, but it is accelerating. If we divide the spring into...
  27. C

    Springs and potential/kinetic energy

    Homework Statement A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. (a) What is the amplitude of vibration? I already solved for...
  28. Bryson Stevens

    What is the spring constant for the bungee cord used in the given scenario?

    Homework Statement A 84.0-kg bungee jumper steps off a bridge with a light bungee cord tied to her and to the bridge. The unstretched length of the cord is 15.0 m. The jumper reaches reaches the bottom of her motion 38.0 m below the bridge before bouncing back. We wish to find the time interval...
  29. B

    Thermal Conductivity of Springs

    I have a question that I've been debating with some co-workers. We are using conical springs (tapered) that most of the time in our application fully compress once engaged. We are measuring minute changes in temperature and I was wondering if a spring diffuses more heat compressed or relaxed...
  30. A

    Simple harmonic motion: mass on a spring is hit by a bullet

    Homework Statement A 4.0kg block is suspended from a spring with force constant of 500N/m. A 50g bullet is fired into the block from directly below with a speed of 150m/s and is imbedded in the block. Find the amplitude of the resulting simple harmonic motion. Homework Equations F=-kx...
  31. T

    AP Physics: Momentum & Springs

    1. A mass M is connected to a wall by an ideal spring. The mass is on a frictionless surface. The mass is pushed toward the wall, compressing the spring by a distance X. Use the impulse-momentum theorem to demonstrate that the mass will reach a maximum velocity of X * (K / M)^1/2. 2. J = delta...
  32. AsadaShino92

    Harmonic motion with damping

    Homework Statement An object of mass 0.2kg is hung from a spring whose spring constant is 80N/m. The object is subject to a resistive force given by -bv, where v is it's velocity in meters per second. If the damped frequency is √(3)/2 of the undamped frequency, what is the value of b...
  33. R

    Amplitude and Vibrations in Springs

    Homework Statement The amplitude of vibration of a mass on a horizontal spring experiencing SHM is = 0.13m. The mass is 85g and the force constant is 55N/m. a) What is the maximum elastic potential energy of the system. b) Find the speed of the mass when it's position is x = 7.4cm from the...
  34. J

    Modeling a Damped Spring System with Differential Equations

    Homework Statement After a mass weighing 8 pounds is attached to a 5-foot spring, the spring measures 6.6 feet. The entire system is placed in a medium that offers a damping constant of one. Find the equation of motion if the mass is initially released from a point 6 inches below the...
  35. C

    Two blocks connected by springs moving in a circle

    Homework Statement Block A and block B are on a frictionless table as shown in Figure 2. Spring 1 connects block A to a frictionless peg at 0 and spring 2 connects block A and block B. Their masses are respectively mA=0:45 kg and mB=0:32 kg. When the blocks are in uniform circular motion about...
  36. M

    Work done in vertical springs & External Agent

    Homework Statement I've encountered an answered problem in this book titled, "Physics for Scientists and Engineers with Modern Physics, 9th Ed" by Serway at page 187. So there is a spring which is hung vertically. 1. The first condition was the spring at an equilibrium state (ΔX=0) 2. The...
  37. B

    Projectile Motion spring launch

    Homework Statement I am trying to find the force needed from a spring to launch a mass of 800g to a length of 0.875m. This launch would be at the optimum angle of 45º. I am aware of all projectile motion equations but am having difficulty linking them to force and thus solving the problem...
  38. wololo

    Springs with Dashpot: Understanding Motion Equations

    Homework Statement Homework Equations ∑F=ma F=-kx x = Ae-γt/2cos(ωt + ∅) The Attempt at a Solution I have looked up this old thread but don't understand how to get the equation of motion from : ma1=-kx1-k(x1-x2) - bv ma2=-kx2-k(x2-x1) - bv...
  39. A

    Statics: four crates, four springs, free body diagram

    Homework Statement In figure (a), four identical crates weighing 2,000 lb each are stacked one on top of another, and in figure (b) a simple model for determining the deformation of the stack of crates is shown. In this model, each spring has the same stiffness k = 4,500 lb/in. and the forces...
  40. Thom_Silva

    A Rotating motor compressing a spring

    Hello, I've recently came across this video (), where the authors use a motor to compress springs and therefore achieve locomotion. I've been thinking why is there a resulting downward net force. But i can't really figure it out. Thank you for time :) See the video from 1.16 minutes and...
  41. T

    Elevator falling on springs

    Homework Statement My question states that an elevator is falling on springs that are supposed to absorb the residual energy if the brakes fail to stop the elevator. They are asking how many springs are needed so that the elevator does not compress the springs by more than 0.2m? mass of...
  42. faithrose123

    Object attached in between two or more springs

    if an object is attached in between two springs, the spring combination is called parallel combinationthen what do you call an object attached in between 1 spring on the left side and 2 springs on the right side of the object,? or an object attached in between 1 in the left and 3 on the opposite...
  43. Daley192303

    Lagrangian of 3 masses connected by springs, non-parallel.

    Writing the Lagrangian for 3 masses and 2 springs in a line is easy. KE=1/2(m*v^2) L=KE(m1)+k/2(l1-(x2-x1))^2+KE(m2)+k2/2[L2-(x3-x2)]^2+KE(m3) However, I wish to model non-linear linkages of the above 3 masses and 2 springs. Suppose that the second spring (m2-m3) is angle θ away from the...
  44. S

    Equations of motion two springs pendulum system

    Homework Statement Give governing equations for the system about its static equilibrium, assuming small vibrations System consists of two springs located under 45 degrees to the vertical (both have same k-value) in undisturbed situation. Lower ends of the springs are attached to each other...
  45. Nicholas Morse

    How to determine length of a spring

    Hi Everyone, Kind of a tough question here. How do I determine the length of a spring if we don't have any visual information about it? All we have is the spring rate & change of object position from when the spring is uncoiled, to fully coiled. Anyone have any ideas on this? I tried the...
  46. Hunter Bliss

    Two Connected Masses Swinging on Two Springs - Classic. Mech

    Homework Statement So in this exercise, two masses m connected by a massless rod with length l are swinging from two springs with constant k and length b. The two springs also make an angle Ө with the vertical. This angle, for this exercise specifically, is very small. (Gravity can also be...
  47. Mayzu

    Maximum extension of a bungee cord

    Homework Statement (a) An 81 kg student is launched from a bridge by his best friends, some 50 metres above the river surface. Fortunately, he is attached to a 30 m bungee cord with a spring constant of 270 N/m. i) What is the equilibrium length of the bungee cord, including the force of...
  48. haruspex

    Frequently Made Errors in Mechanics - Springs - Comments

    haruspex submitted a new PF Insights post Frequently Made Errors in Mechanics - Springs Continue reading the Original PF Insights Post.
  49. W

    Understanding the Debye Model for Solids: Masses and Springs

    Hi! I feel like I've understood none of this stuff! A 1D chain of springs and masses modeling a chain of atoms has a dispersion relation ala ## \omega## ~ ##|sin(k a /2) |##, where ##k## is the wave vector and ##a## the distance between atoms. As far as I have understood, the debye model (in...
  50. L

    The Change in Elastic Potential Energy with Different Spring Stretches

    Homework Statement A spring constant of ##3200 N/m## is initially streched until the elastic potential energy is ##1.44## J (##U=0## for no stretch). What is the change in elastic potential energy if the initial stretch is changed to (a) a stretch of ##2.0## cm, (b) a compression of ##2.0## cm...
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