Questions tagged [oscillators]

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1answer
40 views

Could the flex in a skyscraper due to wind be used to produce power?

While browsing 'Hot Questions' on Stack Exchange I came across this question: Can we use the stored gravitational potential energy of a building to produce power? It got me thinking about the use of ...
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2answers
29 views

Materials used for damping

What type of material should be used for damping? Like my course says ductile materials but then if the damper is deformed it wont be able to be used again, so how does that work? Like why not stiff ...
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2answers
69 views

Energy transfer through damping

When a damper is attached to a bridge, its tuned to the bridges natural frequency. I dont get how will that allow for maximum transfer of energy? And also how will heavily damped systems prevent ...
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1answer
180 views

Applying Kramers-Kronig relation to a simple damped oscillator

I just discovered the Kramers-Kronig relation and am trying to apply it to a simple damped oscillator of the form subjected to an impulse at $t=0$, which is a causal system: $$m\ddot x + c\dot x + k ...
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1answer
122 views

How to obtain the quantization of a simple pendulum using Bohr-Wilson-Sommerfeld rule? [closed]

How to obtain the quantization of a simple pendulum using Bohr-Wilson-Sommerfeld rule?
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1answer
28 views

Small amplitudes and Stokes drag law

Why is it that on a damped harmonic oscillator or a pendulum in a fluid, the Stokes drag law in the fluid only applied to small amplitude oscillation compared to large amplitudes oscillations? Dose ...
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1answer
71 views

To consider or not to consider potential energy of a mass attached to a spring in oscillation? [closed]

For the above system I have the following expressions for kinetic and potential energy: $$ V = \frac{1}{2}\,k\,x^{2}+m\,g\,l\,(1-cos\,\theta)-m\,g\,x\\ T = \frac{1}{2}\,m\,\dot{x}^{2}+\frac{1}{2}\,m\,...
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1answer
21 views

Damped oscilliations on a ball rolling in a U-shape

How do you calculate the rate of loss of energy on a ball moving in a U-shape (half sphere)? Can I simply look at the height of the ball at its peaks and measure the difference between the potential ...
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2answers
43 views

Restoring forces and oscillating systems

My book states, 'Restoring forces give the system it's potential energy.' And it also states, 'Inertia due to mass in mechanical system gives the system it's kinetic energy.' I don't get what is all ...
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2answers
132 views

Why $y=A\sin(kx-\omega t)$ is used in deriving standing wave equation? [closed]

In my text book equation of travelling wave is given as $y=A\sin(\omega t-kx)$ and they deduced standing wave equation using the same wave equation and arrived at $Y=2A\cos(kx)\sin(\omega t)$ but ...
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1answer
163 views

Why is frequency equal to the inverse of period?

I am really struggling with this concept, please help. I know that the period is simply the time for 1 for one complete cycle, but how come the frequency is 1 over this? It is confusing to me
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1answer
68 views

Finding the Amplitude of a Spring Oscillation given initial Position and Velocity

I'm trying to create a physics simulation, and I need to be able to determine the amplitude of the oscillation of a mass-and-spring system given any position that the mass might be in and the velocity ...
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1answer
51 views

Oscillations and Spring balances problem

Problem Statement: A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released oscillates with a ...
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2answers
42 views

Damped drive oscillating systems

I am currently looking at the theory of find the viscosity of and object through damped harmonic motion, and tho it can be done there is obviously a limitation with regrades to the medium. If the ...
1
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1answer
335 views

How to derive a formula for the period of a simple pendulum? [duplicate]

The following formula is given in our lab manual: $$ T = 2 \pi \sqrt{\frac{L}{g}} \left( 1 + \frac{1}{4}\sin^2 \frac{\theta}{2} + \frac{9}{64}\sin^4 \frac{\theta}{2}+\cdots \right) $$ for the period ...
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1answer
34 views

Understanding a reference (Cummins on 2d order ODE)

In the first page of The Impulse Response Function and Ship Motions (Cummins, 1962), it is written that: We can now write an equation, which has the appearance of a differential equation, relating ...
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0answers
41 views

Swing - time taken [duplicate]

I was thinking about how I would go about calculating the time taken for a swing to swing from one side to the other, assuming that there only exists a gravitational force and discarding all other ...
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2answers
113 views

How is the simple damper equation derived?

I know the spring is modeled as $F_{\text{elastic}} = k\cdot x$ when the displacements are small since this is empirically based, but what happens with $F_{\text{damping}}=c\cdot\dot{x}$? It is the ...
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1answer
61 views

Single-mode hamiltonian

I´m a bit stuck with an exercise I have to do for a class of mine. We have been given a Hamiltonian $$\hat{H}=\hbar\omega\hat{a}^{\dagger}\hat{a}+\hbar\theta\left(\hat{a}^2+\hat{a}^{\dagger 2}\right)...
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57 views

How does a sound box amplifier work?

I read in a few places that in a guitar for example, the vibrations are passed through the connectors to the wood and the wood with its bigger surface is more efficient as a coupler to the air, ...
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1answer
80 views

How fast can we walk? [closed]

It has been a common observation that as and when we accelerate ourselves, there comes a point after which we cannot stay on the ground completely. I wanted to know whether we can find such a maximum ...
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3answers
150 views

Is natural frequency of an LC circuit equal to angular frequency? Why don't the units match?

When I was reading the LC circuit in my textbook I came across the derivation of equations of instantaneous charge and current. Which is no problem, but when I got to the derivation to current . It ...
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0answers
68 views

Spring with oscillating support (Goldstein chapter 11, problem 2)

The problem: A point mass m hangs at one end of a vertically hung hooke-like spring of force constant k. The other end of the spring is oscillated up and down according to $z=a\cos(w_1t)$. By ...
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1answer
71 views

Green's Function Method for a Spring and mass system [closed]

I think I've done part a) correctly and I have a general solution. However, I now have two unknown constants in my general solution and, as far as I can see, only one condition ($x(0)=-1$) with which ...
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3answers
77 views

$Q$-factor for damped oscillator (not driven)?

How would this be defined? Some of the Q-factor definitions I have encountered include: $$Q=2\pi\frac{Energy \space stored}{Mean \space power \space per \space cycle}\\Q=2\pi\frac{Energy \space ...
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1answer
126 views

Small Angle Approximation for Simple Pendulum

I am working on a simple pendulum problem. The $y$ direction is vertical and the $x$ direction is horizontal. Displacement in the $x$ direction is taken to be much less than the length of the string, ...
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1answer
193 views

Why is a parallel RLC circuit usually driven by a current source?

Almost always when I see an example of a parallel RLC/LC circuit diagram online, the circuit is driven by a current source instead of a voltage source. On the other hand, the series RLC is always ...
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2answers
264 views

Implementing a spherical pendulum

I am trying to implement a spherical pendulum. The Lagrangian (which I haven't fully understood so yet) based on $l$, θ and φ taken from this page result in the equations: \begin{align} \...
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3answers
49 views

Why do two things lose contact only when normal = 0?

Why do two things lose contact only when normal = 0? For example, I was doing a question in which a massless plank was attached to a spring. The plank also had a block of mass m kept on it. The whole ...
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1answer
36 views

Application of linear constant coefficients ODE of the second order [closed]

I've asked this question in math forum. Apparently this question is not welcomed there. So maybe here I can get a proper response. Consider ODE in the form of $$y''+ay'+by=f(t)$$ where $a$ and $b$ are ...
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2answers
92 views

Complex solutions to an Underdamped Oscillator

In many of the books talking about damped simple harmonic motion, the underdamped oscillator is treated as follows: Newton's second law says $$m\ddot{x} + r\dot{x} + sx = 0 $$where s is stiffness ...
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2answers
52 views

What is the difference between “monochromatic” and “impulse” force?

In a paper I am reading (linked below), the following is stated: The transient motions of the sphere and the gas bubble in the elastic, incompressible, inviscous medium are investigated in response ...
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1answer
33 views

Damped mechanical wave

a string with density $\rho$ and tension $T$ is bound at it's two ends at $x=0$ and $x=L$. there is a force acting on the string proportional to the velocity $F(x,t)= -2\gamma \rho \dot \psi(x,t)$ ...
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2answers
94 views

Professor and textbook disagree on frequency at which a pendulum oscillates

We had a guest lecturer today who told us that the frequency at which a pendulum oscillates is $\omega=\sqrt{mgL/I}$. However the textbook states that is $\omega=\sqrt{g/L}$. Why the discrepancy?
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1answer
53 views

Harmonic oscillators in fluids and driven oscllations

If given a normal spring/mass system and letting the mass oscillate in a fluid say water, would it be possible for the motion of the fluid, if the fluid is moving to create a driven oscillation and ...
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1answer
246 views

Why is the tension in a pendulum string highest when it is at the mean position?

Why does the string of a pendulum have max tension when it is at the mean position?
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2answers
160 views

Impedance Matching in a String

I was reading 121st page of HJ Pain's Vibrations and waves and I saw this with the derivation of impedance matching on a string :- The conditions derived were: The impedance of coupling string be ...
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2answers
189 views

What is an anisotropic harmonic oscillator?

I can't find any explanation of it anywhere in the internet. How is it different from an isotropic harmonic oscillator?
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1answer
44 views

Forced Oscillations and Complex Representation

An oscillating force $F \cos \omega t = \Re\{Fe^{i\omega t}\}$, where $F$ is real, is applied to a mass $m$ on the end of a spring with spring constant $k$. The displacement, $x$, of the particle can ...
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1answer
42 views

Interpreting derivatives

So we have a function such that the distance moved by a particle (say $s$) is proportional to $sin(Ct)$ where $C$ is a constant. Now i needed to show that the rate of change of velocity is directly ...
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2answers
148 views

Significance of the complex component in the underdamped harmonic motion equation [closed]

The following differential equation represents the motion of a body of mass $m$ and displacement $x$ from the mean position, that is attached to a spring of force constant $a$ and viscous damping ...
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2answers
37 views

Do we need a small displacement to create a oscillatory motion on the spring?

Do we need a small displacement to create a oscillatory motion on the spring with a mass attached to it? Whats the limit of the displacement that we can give initally to create a oscillatory motion? ...
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3answers
78 views

Oscillator with decaying restoring force

Suppose a system that is described by the equation of motion: $$ \ddot{x} = -k\cdot x\cdot \exp\left(-\frac{t^2}{2\sigma^2}\right). $$ (For example a spring with decaying stiffness.) I'd like to ...
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3answers
58 views

Contradiction on Oscillating Mass [closed]

A bead is oscillating in horizontal direction as shown in the figure, our aim is to find the angular frequency of the oscillating bead First, we can write the potential as: $$V(l)=\frac{1}{2}k\cdot l^...
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1answer
41 views

Overdamped RLC circuit

I have a series RLC circuit with an equation: $$\frac{d^2I}{dt} + 2\alpha \frac{dI}{dt} + \omega_0^2 I = 0$$ (No outside sources affecting the circuit, only some $I_0$ was in the circuit at the ...
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2answers
541 views

Why does the length of a pendulum cause different natural frequencies of pendulums in Barton's pendulum?

In Barton's pendulum, the pendulum with string that is the same length, L, as the brass bob (source of driving frequency) has natural frequency equals to the bob's driving frequency. The pendulum ...
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1answer
29 views

Why is $Q$ factor an important quantity for electrical oscillations transmitting radio waves?

My textbook says that "$Q$ factor is an especially important quantity for electrical ossicilations trasnmitting radio waves. When selecting radio and television stations it is essential that the ...
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2answers
110 views

Exact equation of exponential curves of underdamped harmonic motion

I was studying the underdamped harmonic motion and got curious about the fact that the decreasing exponentials $\pm Ae^{-\gamma t}$ are good approximations only for light damping $(\gamma<<\...
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3answers
155 views

Why do lighter pendulums come to rest faster than heavier ones?

I've been reading this website, which stated: All pendulums eventually come to rest with the lighter ones coming to rest faster. I have been taught the mass of a pendulum does not affect its ...
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2answers
435 views

What causes clock drift in quartz oscillators?

Usually, computer seem to use quartz oscillators. In contrast to atomic caesium clocks they seem to have a relatively big drift and thus we need protocols like NTP to correct them. What causes this ...