Questions tagged [oscillators]

A mechanical or electronic system or device that works on the principles of oscillation, that is a periodic fluctuation between two things based on changes in energy. These range from abstract models such as a harmonic oscillator to electrical devices such as an LC circuit.

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10
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5answers
2k views

A conceptual doubt regarding Forced Oscillations and Resonance

While studying about the Resonance and Forced Oscillations, I came across a graph in my textbook that is given below:- Now, the author writes As the amount of damping increases, the peak shifts ...
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2answers
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How do you define the resonance frequency of a forced damped oscillator?

Consider a forced, damped harmonic oscillator $$\ddot{\phi} + 2\beta \dot{\phi} + \omega_0^2 \phi = j(t) \, .\tag{1}$$ If I pick a sinusoidal driving force $j(t) = A \cos(\Omega t)$, I find $$\phi(...
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2answers
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Linearized equations

What is $V_{\alpha\beta}$? And what is a symmetric, positive definite potential energy matrix? And why is there a linearized equation like this?
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What's a good textbook to learn about waves and oscillations?

I'm taking a course on waves and oscillations using Crawford from the Berkeley series (out of print excluding international copies), and would like to know if anyone has any suggestions for a better ...
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4answers
154 views

Need help understanding an equation of motion for a pendulum [closed]

I solved the Lagrangian of a simple pendulum (with help from online examples as this concept is new to me) and ended with the following: $$\ddot{\theta}+\omega^2\theta=0$$ But in the example I was ...
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3answers
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Definition of the $Q$ factor?

According to Wikipedia, the $Q$ factor is defined as: $$Q=2\pi\frac{\mathrm{energy \, \, stored}}{\mathrm{energy \, \,dissipated \, \, per \, \, cycle}}.$$ Here are my questions: Does the energy ...
8
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4answers
38k views

Phase difference of driving frequency and oscillating frequency

Suppose a mass is attached to a spring and is oscillating (SHM). If a driving force is applied, it must be at the same frequency as the mass' oscillation frequency. However I'm told that the phase ...
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1answer
556 views

Why is the wave equation so pervasive?

The homogenous wave equation can be expressed in covariant form as $$ \Box^2 \varphi = 0 $$ where $\Box^2$ is the D'Alembert operator and $\varphi$ is some physical field. The acoustic wave ...
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3answers
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Why does a simple pendulum or a spring-mass system show simple harmonic motion only for small amplitudes?

I've been taught that in a simple pendulum, for small $x$, $\sin x \approx x$. We then derive the formula for the time period of the pendulum. But I still don't understand the Physics behind it. Also, ...
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4answers
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Time period of simple pendulum with varying mass

How do you find time period as a function of time for a simple pendulum that is in the form of a hollow sphere that is filled with mercury and there is a hole in the bottom through which the mercury ...
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1answer
24k views

Does damping force affect period of oscillation?

In my physics notes, it has been given that the damping force increases the period of oscillation. I am unable to understand this part. How is this possible? The only relation I know is that as the ...
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3answers
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What is the qualitative cause for a driven oscillator to have a max. amplitude during resonance?

The steady-state motion of a driven oscillator is given by;$$x =\underset{\text{amplitude}} {\dfrac{F_0}{m({\omega_0}^2 - {\omega}^2)}} \cos\omega t.$$ As we see, the amplitude becomes maximum when $$\...
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3answers
826 views

Non-SHM oscillatory motion

How to solve these kind of questions , where $|F| \propto x^2$? How to find time period and velocity type related things to the oscillatory motion? $$m\dfrac{d^2x}{dt^2}=F=-\dfrac{dU}{dx}=-3kx|x|.$$ ...
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2answers
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Period $T$ of oscillation with cubic force function

How would I find the period of an oscillator with the following force equation? $$F(x)=-cx^3$$ I've already found the potential energy equation by integrating over distance: $$U(x)={cx^4 \over 4}.$$...
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2answers
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Motion of charged particle in em wave

What is the direction of oscillation of a charged particle when an electromagnetic wave hits it? I think it would in a circle whose plane is along the direction of em wave and perpendicular to ...
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3answers
696 views

How can $F_0\cos\omega t$ change to $F_0e^{i\omega t}$ in driven oscillator equation?

I have one thing that confuses me on deriving the solution for the Linear Forced Oscillator. Suppose we have the equation as $$ma + rv + kx = F_0 \cos \omega t$$ What confuses me is when the driving ...
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2answers
159 views

Are all oscillatory motions periodic motions?

For example, if a pendulum system in the real world oscillates its amplitude and period will eventually decrease. Does that still count as a periodic motion? Since the motion doesn't have the same ...
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1answer
69 views

Which equation to use for simple harmonic motion?

I recently started studying simple harmonic motion and I came across two equations for the displacement of a particle, as given in my textbook: \begin{align} y &= a\sin(\omega t +\phi)\\ x &= ...
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3answers
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What is the period of a physical pendulum without using small-angle approximation?

What is the expression for the period of a physical pendulum without the $\sin\theta\approx\theta$ approximation? i.e. a pendulum described by this equation: $$ mgd\sin(\theta)=-I\ddot\theta $$ ...
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1answer
184 views

Can we let the lowest of n by equal (lenght and k) springs connected masses in equilibrium move in a siusoid way after giving the lowest a pull?

Imagine we hang n masses, connected by equal springs of equal length and with equal k (suspended on a very high ceiling or whatever what, as long as it doesn't exchange energy with the system). So ...
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1answer
179 views

Neutrino flavor eigenstate interaction with matter

We know that neutrino eigenstates are not mass eigenstate and this therefore produces neutrino oscillations. This is, however, deduced from the fact that the neutrino of one flavor produces the ...
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2answers
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Is angular frequency the same as angular velocity or are they different?

I know there are duplicates. But the answers seem to disagree and also I have more specific questions related to this title. First of all, most questions on this site which ask this question have ...
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3answers
296 views

Sound due to guitar [closed]

My teacher told me that quality of sound depends on shape and size of guitar and its resonator. How does quality depend on that?
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1answer
3k views

Why pendulum does not follow SHM for larger angular displacement?

Considering an ideal case(neglecting drag of air, damping etc.), a pendulum follows SHM if the angular displacement is small (upto 10 degrees). But, for large angular displacement(more than 10 degree),...
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3answers
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What is a mode?

The word mode pops up in many fields of physics, yet I can't remember ever encountering a simple but precise definition. After having searched fruitlessly on this site as well, I feel that even ...
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8answers
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Why are sine/cosine always used to describe oscillations?

What I am really asking is are there other functions that, like $\sin()$ and $\cos()$ are bounded from above and below, and periodic? If there are, why are they never used to describe oscillations in ...
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2answers
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Why aren't the lengths of the bars on a toy glockenspiel proportional to the wavelengths?

As you might already know, frequency of musical notes is arranged in a such a way that if, for example, an A note has frequency of $x$, another A note which is placed one octave higher would produce ...
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3answers
4k views

Frequency of small oscillation of particle under gravity constrained to move in curve $y=ax^4$

How to find the frequency of small oscillation of a particle under gravity that moves along curve $y = a x^4$ where $y$ is vertical height and $(a>0)$ is constant? I tried comparing $V(x) = \frac ...
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2answers
571 views

Caldeira-Leggett Dissipation: frequency shift due to bath coupling

I am trying to understand the Caldeira-Leggett model. It considers the Lagrangian $$L = \frac{1}{2} \left(\dot{Q}^2 - \left(\Omega^2-\Delta \Omega^2\right)Q^2\right) - Q \sum_{i} f_iq_i + \sum_{i}\...
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6answers
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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?
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1answer
786 views

Period of a pendulum [closed]

In the book 'Calculus the Early Transcendetals' at page 776 (7th edition) they give that the period of a pendulum with length $\text{L}$ that makes a maximum angle $\theta_0$ with the vertical is: $$\...
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3answers
960 views

RLC circuit - calculating resonant frequency

If I take a series RLC circuit connected to a battery, the impedance is minimized when $\omega = \frac{1}{\sqrt{LC}}$. I also know that the series RLC circuit is analogous to a damped driven harmonic ...
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2answers
320 views

Neutrino mass and energy question

If a neutrino has mass then it travels less than the speed of light. Suppose I boost myself to the rest frame; i.e. bring it to rest in the laboratory. Now if it oscillates between different states ...
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1answer
1k views

Synchronizing Pendulums

Assume we have a frictionless pendulum of length $l$ with mass $m$. This pendulum hangs from some weightless contraption, which is itself bolted to a platform. This platform can move horizontally in ...
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2answers
209 views

Can photons oscillate?

If you fired a laser at the perfect angle at a mirror (for either mirror setup), and then quickly moved a mirror to replace the laser, will the light oscillate between the mirrors, as shown in the ...
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3answers
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Condition for closed orbit [closed]

I'd like to know when an orbit is closed. I know that, to have a closed orbit, there is a ratio that must be a rational number, but I don't know other things..
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1answer
243 views

Oscillating piston shock waves

I am interesting to know whether there are analytical solutions for a piston gonging like a sine wave and generated shock wave and rarefaction. How the energy change during this process and how can we ...
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1answer
131 views

Why are oscillations so ubiquitous in nature? [duplicate]

I'm aware that you can always approximate a potential by a quadratic term. But is this the most 'fundamental' reason for the pervasiveness for oscillations?
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2answers
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How could this damped oscillator ever go to infinity? Or negative infinity for that matter?

This is an ODE problem,but I cannot visualize why it can go to infinity or negative infinity. Consider $$x'' -6x' + 8x = 0$$ Where $x''$ is acceleration, $-6x'$ is the damping effect and $8x$ is ...
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2answers
360 views

SHM with acceleration at mean position

Suppose we have an equation of motion as $$\frac{d^2x}{dt^2} = -kx + c,$$ then can it be called a SHM? Since acceleration is still proportional to displacement. But then, how will we define the mean ...
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2answers
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Independence of Period and Amplitude in Simple Harmonic Motion

In Simple Harmonic Motion, the period $T$ of an oscillation, is said to be independent of the amplitude $A$ of an oscillation, but why is that so? Attempting to derive from the equations of Simple ...
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1answer
403 views

The actual period of a pendulum at 90°. Looking for the correct formula

Do you have access to any scientific experiment which gives the period of a pendulum when the angle is $90^\circ$: this article says $T$ varies to about $18\%$ up to $90^\circ,$ so for a seconds ...
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3answers
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Is the displacement of a driving oscillator in phase with the driving force?

In a set up such as the following: I have read in many places that below resonance the driving force is in phase with the harmonic oscillator. I have also read that the driving oscillator is in phase ...
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5answers
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Why does pitch increase when you blow harder into a whistle?

When you play recorder or whistle, the pitch depends on how hard you blow into the tube. E.g. when you blow a whistle, initially the pitch is slightly lower when there is less air flow. This seems ...
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6answers
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Simple Pendulum Why Generalized Coordinate Always Angle?

When writing the equations of motion for the simple pendulum, why do textbooks always choose $\theta$ to be the generalized coordinate? The force of gravity is in the y-direction so wouldn't it be ...
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1answer
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Why does $k/m=\omega^2$ for harmonic motion? [closed]

Can anyone please give me a proof for $k/m=w^2$ in simple harmonic motion? I have tried energy conservation and Newton's laws as follows : In the case of a mass-spring system, $$F=ma =-kx\\ F=ma = ...
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1answer
425 views

Does electron have some intrinsic ~$10^{21}$ Hz oscillations (de Broglie's clock/Zitterbewegung)?

Louis De Broglie has postulated in 1924 that with electron's mass there comes some $\approx 10^{21}$Hz inner oscillation: $E=mc^2=h f=\hbar \omega$. We would get such oscillation e.g. if using $E=mc^...
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2answers
901 views

Is the usually taught solution to forced harmonic motion just a special solution?

Let's say we have a mass on a spring being driven by a forcing function. Given hook's law, $F = -kx$, and a forcing function of $$F(t) = F_0\sin(\omega t) .$$ We can write: $$ m\frac{d^2x}{dt^2} = -...
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2answers
165 views

Why we can neglect rapidly oscillating terms in favor of slowly oscillating terms?

I never really understood why we can neglect rapidly oscillating terms in favor for slowly ones. As an example, in my quantum-mechanics studies I ran into this ODE: $$i\frac{d}{dt}\gamma_a = Ae^{i(\...
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3answers
3k views

Non-resonant but efficient frequencies

I understand that if the frequency of a driving force coincides with the natural frequency of an oscillator (say a pendulum), the rate at which energy is transferred to the same is maximized. However, ...