# Oscillator Definition and 29 Discussions

Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.
Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy.

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1. ### I Damped oscillator with changing mass

Hello, So about two weeks ago in class we looked at RLC circuits in our E&M course, and short story short... we compared the exchange of energy between the Capacitor and the Inductor (both ideal) to simple harmonic motion. Once the capacitor and inductor are not ideal anymore, we said it's...

3. ### A Anharmonic oscillators with closed-form solutions

There are some articles from the 1980s where the authors discuss 1D quantum oscillators where ##V(x)## has higher than quadratic terms in it but an exact solution can still be found. One example is in this link: https://iopscience.iop.org/article/10.1088/0305-4470/14/9/001 Has anyone tried to...
4. ### Nonlinear spring made from many different linear springs in series?

Can I create a nonlinear spring, for a nonlinear oscillator, by putting many linear springs in series and parallel?
5. ### Looking for an intuitive explanation for a mass-on-spring simple oscillator's frequency

I just noticed something that is a little bit of a different perspective on a mass-on-spring (horizontal) simple (so undamped) oscillator's frequency and looking for some intuition on it. There are many ways to derive that for a mass on a horizontal frictionless surface on a spring with spring...
6. ### A Oscillator Model with Eigenfunctions

Hi, I have been reading the Milonni and Eberly book "Laser": in one of the chapters they discuss the Oscillator Model. The treatment is quite straightforward, the Hamiltonian of the process is H=H0+HI where the first term is the "undisturbed" hamiltonian, and the second one is the interaction...
7. ### I The allowed energies of a 3D harmonic oscillator

Hi! I'm trying to calculate the allowed energies of each state for 3D harmonic oscillator. En = (Nx+1/2)hwx + (Ny+1/2)hwy+ (Nz+1/2)hwz, Nx,Ny,Nz = 0,1,2,... Unfortunately I didn't find this topic in my textbook. Can somebody help me?
8. ### Trouble with high frequency astable multivibrator

I am having trouble getting an astable multivibrator to oscillate higher than 480 KHz. I added a "baker clamp" which gave some improvement, but didn't get me to the target frequency of 816.5 KHz. I am on an iPad and can't post a schematic. I use 2sc6082-1e transistors and bat41 diodes for the...
9. ### Equation of an oscillating system without any starting values

Homework Statement A mass m1 is located on a platform with mass M. The platfrom is located on springs with total constant k such that it can swing vertically in direction x. a) Write down the equations of motion assuming mass m1 will always be connected to the platform. Write it as x(t) b)...
10. ### How do computers keep time without power?

I know the CMOS battery keeps the time and BIOS settings , but what is powered by the batter to keep time? A crystal oscillator? And why is it so crucial to keep time on a regular desktop computer?
11. ### Normal force as a function of time (oscillator)

Homework Statement A spring with spring constant k is attached to a box of mass M in which is placed a small body of mass m. The system is displaced a distance A from equilibrium and released from rest. Find the normal force between the box and the small mass as a function of time. For what...
12. ### Complex Solutions to Oscillations

Homework Statement Homework Equations The Attempt at a Solution I tried differentiating both sides of 3 and re-arranging it such that it started to look like equation 2, however i got stuck with 2 first order terms z' and couldn't find a way to manipulate it into a function z. I then...
13. ### I Meaning of the word "Harmonic" in different contexts

A harmonic function is one that satisfies Laplace's equation -- a definition cannot be more precise than that. However, in the study of vibrations, sine and cosine are considered harmonic functions; but they don't solve Laplace's equation. And then there are words like: harmonics (for higher...
14. ### Continuous and discrete spectra

Is there any way to convert a continuous, aperiodic spectrum, to a discrete spectrum, in a signal? If so, would part of he energy of this signal be lost, I am this process of conversion, or would it be " distributed" amomg the various frequencies?
15. ### Steady State Solution of Forced, Damped Harmonic Oscillator

Homework Statement A damped harmonic oscillator is driven by an external force of the form $$F_{ext}=F_0sin(\omega t)$$ Show that the steady state solution is given by $$x(t)=A(\omega)sin(\omega t-\phi)$$ where $$A(\omega)=\frac{F_0/m}{[(\omega_0^2-\omega^2)^2+4\gamma^2\omega^2]^{1/2}}$$ and...
16. ### Harmonic oscillator with friction

Homework Statement Spring with spring constant k=2000N/m has an object with mass 10kg attached to it. When it is pulled 0.1m away from the equilibrium state it starts oscillating and came to a stop. The coefficient of kinetic friction is 0.2 and the coefficient of static friction is 0.5. Find...
17. ### I Undamped Driven Oscillation

The equations I'm getting when I solve the differential equations seem to imply that the amplitude of oscillation does not vary in time. For example, if I have x'' + ω02x = cos(ωt) If we suppose that ω≠ω0, then the general solution should look something like: x(t) = c1cos(ω0t) + c2sin(ω0t)...
18. ### Why LC tank only oscillates at resonant frequency?

I am wondering why LC tank only oscillates at resonant frequency not other frequencies? Is there a physics explanation for that?
19. ### Normal modes and degrees of freedom in coupled oscillators

Not a textbook/homework problem so I'm not using the format (hopefully that's ok). Can someone offer an explanation of normal modes and how to calculate the degrees of freedom in a system of coupled oscillators? From what I've seen the degrees of freedom seems to be equal to the number of...
20. ### 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...
21. ### About Crystals in microcontroller......

I have a question that if we use external quartz crystal in Microcontroller and connect it to battery... Crystal gives regular and very accurate electrical frequency... But it should get mechanical vibration from somewhere to give electrical pulses... From where it receives mechanical vibrations?
22. ### Springs with dashpot

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...
23. ### Energy of electron-hole pairs in 3D space

Dear All: I'm trying to use fluctuation dissipation theorem to describe spontaneous photon emission process by electron-hole recombination in semiconductor material. I notice that all the references using such a method considers the dipole's degree of freedom separately, for example in x, y, z...
24. ### 555 timer IC - Calculating resistance needed

Voltage = 9.0 V, Current = 20 mA, Capacitor (C) = 10 microF, Resistance before (too high) [R_A = R_B] = 10 k Ohms. In a a-stable oscillator, calculating the resistance needed for two resistors (R_A = R_B) to discharge and charge a capacitor (C) so that a LED does not blow. Currently my circuit...
25. ### How do you plot eigenfunctions of perturbed HO?

Homework Statement Find eigenvalues and eigenvectors of a perturbed harmonic oscillator (H=H0+lambda*q4 numerically using different numerical methods and plot perturbed eigenfunctions. I wrote a code in c++ which returns a row of eigenvalues of the perturbed matrix H and a matrix of...
26. ### Relationship between size and frequency of an oscillator

I've always just accepted that as you scale down a mechanical system the frequency and Q factor both increase. For example, this Wikipedia page simply says that "Small bells ring at higher frequencies than large bells". But for a driven damped harmonic oscillator, what is the exact relationship...
27. ### Designing a variable-frequency ultrasonic wave generator

Hello everyone! Seeing as this is my first post, I'll give you a basic background of who I am: My name is Andrew Raisbeck; I graduated from university with a Bachelor of Computing (Computer Science) degree a little over a year ago, and I now work full-time for the government of Canada. Since I...
28. ### Wave Generator with Crystal Quartz Oscillator?

Hi All! A little background info. I'm working with cardiac pacemaking devices with the overall scope of implementing piezoelectric energy harvesters into the devices. I'm in the initial stages of research and development. Okay, so this is my conundrum: I have an output pulse circuit as shown...
29. ### First Year Forced Oscillator Problem

Homework Statement Damping is negligible for a 0.164 kg mass hanging from a light 6.70 N/m spring. The system is driven by a force oscillating with an amplitude of 1.77 N. At what frequency will the force make the mass vibrate with an amplitude of 0.500 m? There are two possible solutions...