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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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1answer
192 views

Are spring potential energy and internal energy the same?

From classical mechanics, the force on a spring is given by the negative gradient of the potential energy with respect to position or displacement. Can we also say $F=-\partial U / \partial x$, ...
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1answer
79 views

Factor $1/2$ in work done by spring force [duplicate]

My book says Spring Force = $-kx$ where k is spring constant and x is displacement from equilibrium position. Then it says work done by spring force is $-kx^2/2$. But I know Work Done = Force $×$ ...
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3answers
108 views

Why does different part of a spring having mass expand proportional to their distance while the spring has some mass hanged in the bottom?

Why do different parts of a massive spring expand proportional to their distance while the spring has some mass hung on the bottom which is comparably very less than the mass of the spring? If we take ...
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2answers
86 views

What happens if we apply different forces in opposite directions on both ends of a spring?

I'm confused about this... If I have a spring and I apply force F1 towards the right on the right end and F2 towards the left on the left end, what will happen? There are no blocks, just a light ...
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1answer
43 views

Motion along length of a spring [closed]

What's relation between velocity of each part of a massive spring undergoing Simple Harmonic Motion.
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1answer
171 views

Finding the frictional coefficient

This is going to be very long question. A 1 kg block situated on a rough incline is connected to a spring constant 100Nm as shown in fig. The block is released from rest with the spring in the ...
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1answer
75 views

Mass attached to spring - elastic potential energy

I am looking at a problem in which a mass $m$ is attached to the midpoint of a light elastic spring of natural length $2l$ and then released. The two ends of the spring, $P$ and $Q$, are at the same ...
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1answer
157 views

Spring Constant of Two-Sided Fixed Beam [closed]

Let's suppose I have a two-sided fixed beam: ...and I want to find the equivalent spring constant... can I do the following: I know that the maximum deflection (at the center is): $$\delta =\frac{...
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2answers
391 views

Why is the restoring force not zero at the equilibrium position of simple harmonic motion?

The restoring force is applied in order to take the body it's equilibrium. Then in a SHM why in the mean position restoring force maximum rather than being zero as it has reached equilibrium. (After ...
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203 views

Centripetal Force on Springs

Please could someone provide an explanation for this. I thought that increased velocity would cause greater centripetal force (which, I think, acts towards the centre of curvature) so would the ...
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2answers
125 views

Heisenberg's Uncertainty Principle for 2 bodies connected by a spring

Take two identical particles, measure there mass and let them spring apart. Now the two particles will move in opposite direction. If I calculate accurately position of first particle and velocity of ...
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2answers
90 views

Tension of the rope, error in the book's solution? [closed]

I'm stuck on getting the solutions the professor gave us for this problem. First of all the figure: He asks us for the maximum tension $T$ of the rope between $m_!$ and $m_2$. His solution: $$T = ...
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2answers
304 views

Rod connected to springs. Can this oscillate if the rod has no mass?

My thoughts led me to change the question's title. Here's what I've tried in solving the problem and led me to ask the question in the title. We have the following diagram where the beam has no mass ...
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1answer
418 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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1answer
54 views

Why does $g$ show up in the frequency of this oscillation?

The problem diagram is given in the picture below: Having looked at this question Why does the acceleration $g$ due to gravity not affect the period of a vertically mounted spring? something troubles ...
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1answer
456 views

Simple harmonic motion with pulley with mass

The problem is presented in the following diagram I'm refreshing things I've already learnt and I know I have some major gaps but I've searched and haven't managed to find a similar problem. The axis ...
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1answer
813 views

Question on capacitor and springs

The question is as follows: One of the plates of a charged parallel plate capacitor is connected to a non conducting spring of stiffness K while the other plate is fixed. The other end of the ...
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0answers
43 views

Potential gravitational energy versus potential spring energy [duplicate]

My textbook points out the following predicament, and I do not know the answer, despite a lot of thinking: A spring is hanging of a ceiling and a mass is attached. As a result the spring descends to ...
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1answer
198 views

Spring-Block system [closed]

Here is a multiple spring and a block system. I need to find the maximum elongation of the spring. I tried to take $mg-(k_1+k_2)x=0$, and find $x$ from there. The answer is coming wrong. It should ...
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2answers
124 views

why work done by spring is negative eventhough KE increases? [closed]

Suppose a block is attached to a compressed spring, it is released so moves under spring force of magnitude $kx$, let it moves from $-a$ (negative since displacement is negative for a compressed ...
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2answers
98 views

Can an accelerated spring in static equilibrium in its rest frame have different forces at each end?

Let's say I have two identical masses connected by a spring: If F1 = F2 = F then the forces on either end of the spring are also F when the whole arrangement reaches static equilibrium. Now if F2 >...
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3answers
721 views

Gravity’s effect on a vertical spring-block simple harmonic oscillator

I just found a question in my textbook which asked how the period of the vertical oscillation will change if the spring and block system is moved to the moon, and the gravity due to acceleration is ...
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2answers
149 views

meaning of “sufficiently small” in approximations to behaviour of a Harmonic Oscillator

So in my classical mechanics book it states: "For any sufficiently small displacement, any system of this kind behaves like a harmonic oscillator." When discussing SHO. So I am curious what is ...
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2answers
78 views

Spring force that grows not proportional to displacement

Do springs that change their proportionality 'constant' as a function of their winding number per length? I want a spring that obeys $F(x)=kx^2$ instead of $F(x)=kx$. To my intuition if I decrease ...
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1answer
223 views

Why do materials obey Hooke's law? [duplicate]

Why do materials extend proportionally to the force exerted on them (Hooke's law)? I thought that when materials are compressed or extended under force, their atoms become closer or further apart; ...
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2answers
87 views

Spring and mass system

Suppose I have a two masses attached with a spring on ei either side and one of the masses is kept in contact to the wall like in this diagram with friction neglected everywhere. Now when the wall ...
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1answer
48 views

Phase shift of damped mass on spring with moving source [closed]

I have a setup with a moving (upwards, downwards) board on which there is a spring mounted on the edge. The spring has a mass $m$ on its end and is damped in some sort of liquid. What methods could I ...
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1answer
169 views

Why does pseudoforce act in opposite directions when we move from ground frame to the centre of mass?

In the solution of above question, they solved it by moving from ground frame to the frame of centre of mass. But we know that, to move from one frame to another ,we have to subtract the mass-...
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1answer
138 views

Would a spring ever stop?

It is not difficult to show from Newton's second law $$m\ddot x = -kx - b\dot x $$ that an underdamped spring has the equation of motion quantified by $$x(t) = c_1e^{-\beta t}\sin\left(\omega t\right) ...
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2answers
105 views

Vector notation - work done by spring force

I am confused about the work done by spring force in vector notation dW=F.dS , where dW= small work done, F=Force , dS= displacement. Suppose spring is kept along x axis and tied at one end by wall (...
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1answer
380 views

Spring Displacement

I am having trouble understanding the sign/direction of displacement for the equation F=-kx. I am not going to elaborate on what the specific problem is that goes along with this visual since that's ...
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2answers
120 views

Mass hanging by a spring [closed]

I have a mass hanging from the ceiling by a spring, with costant $k$, and wih gravity $g$. Using analytical mechanics I got to the differential equation: $$ \ddot{x} + \frac{k}{m}x + g = 0 $$ The ...
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1answer
126 views

Forces of a rubber band around a cylinder? [closed]

If I have two rubber bands and two cylinders, one smaller in circumference than the other in each case. What circumference does the smaller rubber band need to be in order to apply the equal force in ...
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3answers
2k views

Springs in parallel store less energy than springs in series … but where does the excess energy go?

Two springs in parallel with a weight of 15 N will stretch a certain amount, while the same two springs arranged in series will stretch more under the same weight and so store more energy. I'm fine ...
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0answers
41 views

Simple Harmonic Motion - spring with mass [duplicate]

I'm reading about the following set-up: We have a body of mass $m$ attached to a spring. The restoring force is proportional to the displacement of the body from equilibrium. Using Newton's 2nd law ...
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1answer
48 views

Direction of friction for damped harmonic oscillator

When we study motion of springs, the force of damping(friction) is sometimes opposite to spring force (while returning to the equilibrium) and othertimes spring force is in the direction of friction ...
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0answers
146 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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1answer
52 views

Terms in the stress-energy tensor of a pair of masses coupled by a Hooke oscillator

Think of the simplest system that can be constructed with masses and non-gravitational forces that keep the system bounded: Two masses bounded by a hook spring: $$ T^{\alpha\beta}({\bf x},t) = \...
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1answer
2k views

Can Hooke's law be derived?

Can we derive Hooke's law from the theory of elasticity? I know it is not a fundamental law and therefore can be derived from more basic considerations.
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1answer
102 views

Why is the potential energy of spring negative while it's positive for a dipole?

Potential Energy is the work done against the conservative force As the definition suggests , for a spring $$ U= -\int F \cdot \mathrm{d}x \,.$$ But for a dipole placed in an electric field $$ U= \...
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1answer
119 views

Is there a conservative force acting on a spring that oscillates in SHM?

If I were to stretch a spring, then I am doing positive work in order to increase the potential energy stored in the spring. Since the equation for the potential energy in this case is given by $$U(x)=...
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2answers
180 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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1answer
208 views

Spring oscillator and time dilatation

Consider the mass M suspended on the (ideal) spring with stiffness D, whose suspension point is in rest in inertial frame K'. I understand how the principle of relativity requires that this harmonic ...
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2answers
92 views

Formula for spring constant $k$ [duplicate]

Is there a formula for the spring constant $k$ which satisfies the equation $$F=k\Delta \ell~?$$ A similar question was asked but was answered by transposition of this equation... I'm hoping for an ...
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1answer
71 views

Spring non-linear behavior for small forces

While writing a report about a classical spring experiment I noticed that, if small forces were applied to our spring, this would stretch much less than expected. Searching on the internet I've kinda ...
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3answers
149 views

What is the motion of a mass 'circling' a spring?

Consider a situation whereby there is a mass connected to a spring which is initially unstretched and the system lies on a horizontal plane. An impulse is then applied to the mass giving it an initial ...
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3answers
452 views

Calculating angular frequency for solid disk/spring system

I have a solid disk with radius $R$, mass $M$, and moment of inertia $I = \frac{1}{2}MR^2$ which can freely rotate about a fixed mass in its center. A spring with spring constant $k$ is attached to ...
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0answers
103 views

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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2answers
64 views

How are these equations for energy compatible?

I have one equation that says the energy in an oscillating spring with a mass $$E = 2\pi^2ν^2A^2M.$$ I have another equation that says the energy is the system is quantized $$E = nhν.$$ How are ...
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1answer
146 views

Spring constant, but intrinsic to material, not rest length

If you have two metal springs that are coiled in the same way, but one is twice the length of the other, the spring constant will be half as large for the longer one. That makes sense of course. What'...