All Questions
Tagged with harmonic-oscillator spring
274
questions
15
votes
5
answers
7k
views
Why are springs better at pulling than pushing?
We learnt that a spring stores and releases energy in either direction from the resting position when extended by some distance. When I tried doing this is real life by creating a very low friction ...
11
votes
4
answers
3k
views
Why can all solutions to the simple harmonic motion equation be written in terms of sines and cosines?
The defining property of SHM (simple harmonic motion) is that the force experienced at any value of displacement from the mean position is directly proportional to it and is directed towards the mean ...
- 1,103
11
votes
2
answers
5k
views
Understanding transverse oscillation in 1 mass, 2 spring systems
Lately I have been working through some nice problems on mass-spring systems. There are tons of different configurations - multiple masses, multiple springs, parallel/series, etc.
A few possible ...
- 111
10
votes
6
answers
35k
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Why does the acceleration $g$ due to gravity not affect the period of a vertically mounted spring?
For a vertically mounted spring, I was looking at the formula $ T= 2\pi \sqrt{m/k}$ for a period. Why doesn't the gravitational acceleration $g$ factor in?
- 265
8
votes
3
answers
630
views
Experimental Result Cannot Be Explained by Theory for 2 Spring 1 Mass System
We have 2 spring 1 mass system in 2D as shown,
Here is my brief attempt of solution:
$$\vec{F_x} = \vec{F_{1x}} + \vec{F_{2x}}= -k (x + l) \hat{\imath}- k (x-l)\hat{\imath} = -2 k x \hat{\imath} \...
- 185
7
votes
2
answers
3k
views
Forced harmonic oscillator with two springs
Consider a vertical system of two springs in series, with a mass(50 g) between them. From below the system is driven by a vibration generator. The setup is shown here, but the picture is taken while ...
- 73
7
votes
1
answer
572
views
Finding coefficient of proportionality
Recently in my AP Physics class I did a lab in which I measured k for a spring by setting up an oscillating system with it, and timing the period, repeating for different masses. Since $T=2\pi\sqrt{\...
6
votes
3
answers
529
views
Non-linear spring systems
I've recently been re-learning some physics, and a question came to me when looking over Hooke's law:
In the following I am always assuming that the force required for permanent deformation is ...
- 63
6
votes
2
answers
7k
views
Position of two blocks connected by a spring as a function of time
Two blocks A and B are connected by a spring of spring constant $k$. $A$ is imparted an initial velocity $u$ towards the right along positive x-axis. If $B$ were fixed then the motion of $A$ could be ...
- 61
6
votes
1
answer
6k
views
Effective mass in Spring-with-mass/mass system
Suppose you have a particle of mass $m$ fixed to a spring of mass $m_0$ that, in turn, is fixed to some wall. I'm trying to calculate the effective mass $m'$ that appears in the law of motion of the ...
- 4,594
5
votes
4
answers
859
views
What is the "spring" and what is the "mass" in a loudspeaker system? [closed]
I've been reading about how speakers work and keep seeing that it is analogous to the mass on a spring system.
I'm trying to identify what is the "mass" and what is the "spring" in ...
- 937
5
votes
3
answers
787
views
Is it true that spring has more force acting on it at its positive maximum amplitude than than at the negative one?
Am I missing something?
It seems obvious to me that at $+A$ and $-A$, the spring has restorative forces equal in magnitude but opposite in direction.
But since gravity is always pulling it down, the ...
- 1,341
5
votes
3
answers
9k
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Does amplitude affect time period for spring mass system?
I know that with the formula $T=2\pi\sqrt{\frac{m}{k}}$ the time period is not related to the amplitude. However, would amplitude matter if i do this experiment in real life. Would a greater amplitude ...
- 157
5
votes
2
answers
1k
views
Tricky spring on a surface question
I have this relative simple-looking question that I haven't been able to solve for hours now, it's one of those questions that just drive you nuts if you don't know how to do it.
This is the scenario:
...
- 179
4
votes
2
answers
2k
views
Why does a spring mass system oscillate?
For simply harmonic motion,
acceleration $= -\omega^2 x$, where $\omega$ is the angular frequency.
Within limits of Hooke's law,
the restoring force on the spring is given by
$$F= -k \cdot x$$
This ...
- 45
4
votes
3
answers
64k
views
How to derive the period of spring pendulum?
So I wanted to find out how to (simply, if that's possible) derive the formula for a period of spring pendulum: $T=2\pi \sqrt{\frac{m}{k}}$. However, Google doesn't help me here as all I see is the ...
- 151
4
votes
2
answers
4k
views
Spring-Mass-Pendulum "via Newton's Laws"
Good Night everyone:
I have one problem here that I KNOW how to solve using Lagragian Dynamics. But, I really want to know how to solve using Vector decomposition, Newton's Laws, first-year physics ...
- 3,075
4
votes
2
answers
10k
views
Why is the damping force on a spring oscillator linearly dependent on velocity?
If you consider the damping force is friction like in:
then the force should be $$F=\mu N$$ where $\mu$ is the coefficient of kinetic friction. Why then is the damping force assumed to be linearly ...
- 1,740
4
votes
1
answer
998
views
Faster than critical damping for harmonic oscillator?
The image below shows damping for spring oscillator with Hooke law F=-kx and damped with F=-cv where:
k is spring constant
x is oscillator position
c is damping coefficient
v is velocity of oscillator
...
- 855
4
votes
1
answer
480
views
Simulating quantum network of harmonic oscillators
Let's say that I have a system of $n$ particles $p_1,\ldots,p_n\in\mathbb{R}^3$ (where $n$ here is on the order of 10,000). Furthermore, suppose we have a graph $G=(V,E)$ describing some network, ...
- 325
4
votes
2
answers
272
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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 ...
3
votes
3
answers
2k
views
Spring pendulum - why is it possible to use this equation?
It is known that, when we describe the spring pendulum, we are bound to use the formula
$T = 2\pi \sqrt{m/k}$, however, we can go further and set
$\omega = \frac{2\pi}{T}$
I ponder why is this ...
- 231
3
votes
1
answer
712
views
Where is the energy going in this simple harmonic motion
Suppose i have a block of mass $M $ performing simple harmonic motion under a spring. Now suppose i gently place a particle of mass $m $ on top of it.
Case 1
The mass $m$ is placed when block of mass $...
- 369
3
votes
2
answers
324
views
Undamped oscillations. Why is the solution a linear combination of $\sin()$ and $\cos()$?
$ma = mg - cx$, where $x(0) = x_0 = 0$ is the position in which there is no tension in the rope. $dx/dt = v_0$ for $t = 0$; $v_0$ is a known constant.
The discriminant of the characteristic equation ...
- 680
3
votes
3
answers
146
views
Oscillation of a spring and added mass
Why do we need to add a mass to a spring to make a simple harmonic motion in it? Why can't only a spring 'without a mass' make a simple harmonic motion when we apply an external force?
- 41
3
votes
2
answers
4k
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Measuring young's modulus from simple harmonic motion with cantilever
I was doing this experiment:
http://practicalphysics.org/shm-cantilever.html
I'm interested in the derivation of the result $ω^2 = \frac{Exy^3}{4ML^3}$.
I tried to think where it comes from.
Let's ...
- 171
3
votes
1
answer
7k
views
Kinetic energy and potential energy variation over distance in SHM
When you compute the average potential energy of a horizontal spring mass system from the mean position to the positive amplitude A, the value comes out to be $\frac{1}{6}kA^2$. For the average ...
- 677
3
votes
3
answers
1k
views
What is the significance of clamping the center of the spring?
7. A block is hung on a spring, and the frequency $f$ of the oscillation of the system is measured. The block, a second identical block, and the spring are carried in the Space Shuttle to space. The ...
- 359
3
votes
1
answer
850
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;
...
- 133
3
votes
1
answer
1k
views
Simple harmonic oscillator system and changes in its total energy
Suppose I have a body of mass $M$ connected to a spring (which is connected to a vertical wall) with a stiffness coefficient of $k$ on some frictionless surface. The body oscillates from point $C$ to ...
- 169
3
votes
1
answer
74
views
Mass added to a oscillating spring block system changes the energy stored in the spring [duplicate]
If a block B is attached to a spring and oscillates with amplitude $A_1$. Another block A is added on the block B at equilibrium phase.
At equilibrium, the net force acting on the block B is zero. So ...
3
votes
1
answer
300
views
Spring constant of tuning fork
I was playing with a tuning fork and got to wondering how to find it's spring constant (assuming damped oscillation). I can find plenty of resources about materials for springs, but not a whole lot ...
- 133
3
votes
1
answer
548
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 ...
- 522
3
votes
2
answers
591
views
Energy in simple harmonic motion ─ where is the kinetic energy stored, and where is the potential energy?
When a mass connected to a spring is in simple harmonic motion and somewhere between the mean and extreme positions the mass is cut from spring. Then instantaneously after cutting the mass will only ...
- 31
3
votes
1
answer
191
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? ...
- 199
3
votes
1
answer
4k
views
Damping coefficient and damping ratio [duplicate]
I am not sure if I understand the term damping coefficient correctly (I am a high-school student). Here's the link for the info that I learned:
http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html
...
- 43
3
votes
2
answers
11k
views
How to determine viscous damping coefficient of spring?
I'm trying to determine the viscous damping coefficient of a spring $c$. Read about it on Wikipedia here.
The two equations which I have are:
$f=-cv$ and $ma+cv = -kx$
I know the spring constant $k=...
- 373
2
votes
1
answer
147
views
How to find particular solution to this system of two masses connected by a spring with constant applied forces? Does an analytic solution exist?
This question comes from review I'm doing on my own, so it's not any homework question. I thought this question would be easy to solve, but I seem to be stuck and I am having second thoughts, so I'm ...
- 8,346
2
votes
4
answers
5k
views
Why does the spring constant not depend on the mass of the object attached?
It is said that:
$$ F = -m\omega^2 x = -kx, $$
so $k=m\omega^2$. Since $k$ is the spring constant it doesn't depend on the mass of the object attached to it, but here $m$ signifies the mass of the ...
- 662
2
votes
4
answers
577
views
Why will this system execute simple harmonic motion?
For a particle to exhibit simple harmonic motion, the force acting on it always has to be $\vec{F} = -k\vec{x}$. But here:
Let's say it has some initial elongation. Now, the only way it would have $\...
- 1,096
2
votes
2
answers
1k
views
Extra energy in dual mass-spring systems
Below is a Dual mass spring system placed on a smooth surface(no friction), let us assume the spring constant as $k$ in this case.
Now if we create a small extension in the spring of value $x_o$, the ...
- 189
2
votes
1
answer
692
views
Better understanding natural resonance frequency and simple harmonic motion
Let me see if I'm getting this understood correctly. I'm trying to make sure my interpretation of simple harmonic motion is the right interpretation, including my take on resonant frequency.
Okay, so ...
- 3,192
2
votes
2
answers
253
views
When to use reduced mass?
I have conceptual doubts on when to use the reduced mass.
This is the situation. I have a spring with two charges of mass $m$, each attached to one end of a spring so that
$$ \mu a = -kx $$
from which ...
2
votes
2
answers
3k
views
How to calculate damping ratio or critical damping of a system with two springs and a damper (or two springs and two dampers)?
Background
For a simple system where you have a mass attached to a spring and damper in parallel:
We can calculate the critical damping from the equation of motion:
$$mx_{tt} + cx_t + kx = 0$$
$$ms^2 ...
- 321
2
votes
1
answer
772
views
Confusion between superposition of SHMs
I am a high school student and i am little confused between superposition of Simple harmonic motions{SHM's}, suppose a spring of spring constant $k_1$ has time period $T_1$ and another spring of ...
- 450
2
votes
1
answer
366
views
Motion of $n$ bodies connected with springs
Let's consider $n$ cuboids moving without friction, each of mass $m_i$. Each wo neighboring cuboids are connected with a spring of the coefficient $k$.
...
- 567
2
votes
2
answers
744
views
Interpreting the Negative Sign in Simple Harmonic Motion
What I Know:
$$ \vec F = -k \vec x $$
where the negative sign indicates the Force acts in the opposite direction to the displacement.
If we were to take the integral so...
$$\int_{x_i}^{x_f} Fdx = -\...
- 409
2
votes
3
answers
7k
views
Gravity’s effect on a vertical spring-block simple harmonic oscillator
I just found a question in my textbook which asked how the period of the vertical oscillation will change if the spring and block system is moved to the moon, and the gravity due to acceleration is ...
- 21
2
votes
1
answer
3k
views
General solution of a mass spring system
This is the differential equation that describes small amplitude vertical oscillations of a mass $m$ that is hanging from a spring
$$\frac{d^2x}{d t^{2}} + \frac{b}{m}\frac{dx}{dt} + \frac{k}{m} x = 0$...
- 23
2
votes
1
answer
701
views
Proving Simple Harmonic Motion (direction of acceleration)
A particle of mass $m=0.5kg$, is attached to a spring of natural length $l=0.6m$ and modulus of elasticity $\lambda=60N$, and the setup is on a horizontal smooth table. The other end of the spring is ...
- 6,907