What is Oscillation: Definition and 767 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.
I'm doing a personal experiment where I take a conical spring (that is, a spring with two different diameters on either end), hang it from the ceiling, and measure the period of oscillation for different masses hanging below the spring. I do this for two different orientations of the spring; one...
For my academic research project, I am studying the oscillatory of magnets attached to extension springs. And to have variety of data on different types of oscillation, I'll be using different spring constants as a variable. But in order to get the springs I need to know the dimensions of the...
[Mentor Note: Two duplicate threads merged...]
in container with dimensions L×D, rests water of height H and density ρ. we disturb the water along L dimension, and accept an oscillation is caused on the free surface of the water, which maintains its flatness, so that the central of mass of the...
My professor was teaching me about the superposition of two waves and after this derivation, he marked ##2Acos(\frac{dk}{2}x -\frac{d\omega}{2}t)## as the oscillation part and ##sin (Kx-\omega t)## as the oscillation part, I don't understand why? Any answers regarding this would be considered...
I am using pasco's gravitational torsion balance https://www.pasco.com/products/lab-apparatus/fundamental-constants/ap-8215 to find the universal gravitational constant in a lab report.
Two large tungsten masses are positioned close to two smaller masses, causing the torsion balance to...
If I were to tie a friend of mine adjacent to the oscillating charge and make him oscillate in parallel to my oscillating charged particle such that to him the oscillating particle is at rest, would he observe the generation of electromagnetic waves.
Hi,
so of course Φ0 = 15° and after solving after solving Φ(t=5*T = 5/f) I found γ = 0.012
I need help with b).
If I do 2° = 15° * exp(-0.012t)*cos(2πf*t), I'm not able to find t so I did something else by assuming that the amplitude decreases at a constant rate:
After 5*T = 5*1/f = 18.52 s...
The relevant equations has been me working out the gravitational potential energy. I was told to take the derivative twice from here, but I do not understand why. It leads into a taylor series expansion, which seems excessive, but I was not informed on any other way to do it. Any advice would be...
Hi;
This is in fact not a homework question, but it rather comes out of personal curiosity.
If you look at the graph of the two functions in the image attached, what is the simplest functional representation for such a symmetrical pattern?
Perhaps that's a very dumb question, but I'm having a hard time to understand why it's possible to omit parts of the equations in solving various problems involving oscillations. Here, for example, the complete equation for acceleration is not used (the part with cosine doesn't appear) and here...
I was thinking about how various objects would slide down on an inclined plane, and I just couldn't figure this problem out.
So let's say I have this screw or cone on its side, on an inclined plane. If friction exists, what would the motion of the screw be as it slides down the inclined plane...
(a) By setting up a coordinate system with the x-axis pointing to the right and the y-axis pointing downward we have ##\begin{cases}-kx_{eq}+T_1+F_{s}=0\\ -RF_{s}+rT_1=0\\ r_p (T_2-T_1)=0\\ -T_2+mg=0\end{cases}\Rightarrow x_{eq}=\frac{mg}{k}\left(1+\frac{r}{R}\right)## which coincides with the...
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...
Does mechanical watch ticks slower when move fast, due to relativistic effects?
To make watch tick slower you must change oscillation of balance wheel inside watch, so if answer is yes, what myster "force" change balance wheel oscillation in mechanical watch to ticks slower?
Hi, all
I am experimenting with audio amplifiers for a while now. I learned how to do an operational amplifier with discrete components and understand all its section and sub-circuits, recently. Then I decided to just skip the hard part and use operational amplifier and output power stage for an...
[This is a reference request.]
I'm dissatisfied with the "proofs" I've found so far. E.g., in Kayser's review from 2008, in the paragraph following his eq(1.4), he assumes a propagation amplitude Prop##(\nu_i)## of ##\exp(-im_i \tau_i)##, where "##m_i## is the mass of the ##\nu_i## and...
I'm trying to find the quality factor of a damped system.
I know 3 points from the graph, ##(t,x): (\frac{\pi}{120},0.5), (\frac{\pi}{80},0), (\frac{\pi}{16},0)##
From this I found that ##T = \frac{\pi}{20}##
##\omega_d = \frac{2\pi}{T} = 40 rad##
Then, from the solution ##x(t) = A_0...
1) By conservation of mechanical energy we have ##m_2gl(1-\cos(\alpha))+m_1gl=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2+m_1gl## and by conservation of linear momentum along the x-axis we have ##m_1v_1+m_2v_2=0## which gives us ##v_2=\sqrt{\frac{2m_1gl(1-\cos(\theta))}{m_1+m_2}}## and...
h = d1 + 0.08
d1 = h - 0.08
d2 = h + 0.08
I of the vertical portion
= 1/12 m (l^2 + b^2) + md1^2
= 1/12 m (0.28^2 + 0.04^2) + m(h - 0.08)^2
I of the horizontal portion
= 1/12 m (l^2 + b^2) + md2^2
= 1/12 m (0.28^2 + 0.04^2) + m(h + 0.08)^2
The moment of inertia for the whole T-shape about...
I know that there is phase delay in damped driven oscillation but I want to know is there any phase delay in undamped driven oscillation when we apply sinusoidal driving force. When driving force is maximum, displacement is also maximum as well right?
Take rightwards as positive.
There are 2 equations of motion, depending on whether ##\frac {dx} {dt} ## is positive or not.
The 2 equations are:
##m\ddot x = -kx \pm \mu mg##
My questions about this system:
Is this SHM?
Possible method to solve for equation of motion:
- Solve the 2nd ODE...
Hi,
I have a 3 mass system. ##M \neq m##
I found the forces and I get the following matrix.
I have to find ##\omega_1 , \omega_2, \omega_3## I know I have to find the values of ##\omega## where det(A) = 0, but with a 3x3 matrix it is a nightmare. I can't find the values.
I'm wondering if...
Hello! This is probably something simple but I am getting confused about it. Assume we have an electric field along the z axis given by ##E = -kz##, with ##k>0##, so the field on both sides of the xy-plane points towards the origin. Let's say that we have a positively charged ion at the origin...
My attempt,
Considering that it jumps in the maximum compression position:
$$\frac{kA^2}{2} = mg(H+A)$$
replacing k / m with w ^ 2 :
$$A^2 w^2-2gA-2gH=0$$
Solving the second degree equation:
$$A=\frac{2g+\sqrt{4g^2+8gHw^2}}{2w^2}$$
But the answer is...
so what I did was e^-(1/10.1)=0.9057
and e^-(1/14.8)=0.93466
Then 0.93466/0.9057 = 1.03198, so the heavier mass dampens 1.03 times more than the lighter mass. If the lighter mass decreases the oscillation to 72.1%, then the heavier mass would be 72.1%*1.03198 = 74.4, but this is wrong. It...
So first I found what b/2m is and got 0.287129. Then I found what the sqrt part of the equation was and got 1.128713. Then I added them together to find w. Then I divided by 2pi to find frequency and got 0.255, but the answer is 0.180.
Since its critically damped that means k/m=(b/2m)^2, which would mean w=ib/2m. So m=ib/w. My issue now is that I need to find work.
I could put w back into x(t) to get Ae^((-b/2m)t+phi). I guess I could make this Acos((-b/2m)t+phi)). But I am kinda lost at this point. Sure, I could find the...
Hi,
I have a particle on a parabolic surface $$y = Ax^2$$ and I have to show that the frequency is $$\omega = \sqrt{2Ag}$$
I don't know how to deal with a parabola. I don't think I can use the polar coordinates like a circle.
I don't see how to start this problem and in which coordinates...
When an oscillator produces waves - let's say they are highly focused - that are damped by a second negative phase oscillator, where is the wave energy? The energy in each set of waves must still exist. Has it become hidden?
So since V(cap) + V(ind)=0 then Q/C + L dI/dt=0
Now since I=dQ/dt, I can replace dI/dt with d^2Q/dt^2 resulting in Q/C + L d^2Q/dt^2 =0
Now L d^2Q/dt^2 looks like a harmonic motion thing I can solve, where w^2=L. This means I can find w. I get 0.0005385.
Now my issue is using this w gives the...
Hello! Assuming we have a 2 level system (e.g. an atom with 2 energy levels) and the lifetime of the upper level can be neglected, if we make the atom interact with a laser at a fixed frequency, we would get Rabi oscillations (assume the laser is on resonance). Would we still get Rabi...
In high school I learned about three kinds of motion in classical mechanics - translation, rotation, and oscillation. Are there any other kinds of motion in the physical world?
The hint says to use the moment of inertia of the rod, however i have not covered this on my course and I don't know what it is.
After googling moment of inertia of a rod I found that it is a quantity expressing a body's tendency to resist angular acceleration, and for a rod I=1/3ML^2.
So...
I couldn't prove the first one but i tried to find the period
F = -dU / dx
= - d( U0tan^2( x / a ) ) / dx
= - U0 ( ( 2 sec^2( x / a ) tan( x / a ) / a )
with F=d^2x/dt^2, tan(x/a)=x/a we have
d^2x/dt^2 + U0 ( ( 2 sec^2( x / a ) ( x / a^2 ) =0
from there i don't know how to handle the...
Hello!
So my main and first problem about this question is, I do not know what the problem is about. What I mean by that is, in class we talked about pendulums and are given formulas and assignments regarding pendulums. But this problem here does not seem like it has anything to do with...
I've been trying to continue my education by self-teaching during quarantine (since I can't really go to college right now) with the MIT Opencourseware courses. I landed on one section that's got me stuck for a while which is the second part of this problem (I managed to finish the first part...
From Gauss's Law
give ##E=\dfrac{\sigma}{2\epsilon_0}##
##\therefore P_e=\dfrac{\sigma^2}{2\epsilon_0}##
Consider at equilibrium (before bubble being charged)
##P_i=P_0+\dfrac{4S}{R}##
Using Newton's 2nd Law
##\Sigma F=m\ddot{R}##
Let ##R+\delta R## be the new radius
Give (after binomial...
I am not sure if i get the problem, but if i understand, we want to know the period of oscillations on a spring with length l/3.
If is this the right interpretation, i would say that the stiffness of the new the spring is k/n, where k is the stiffness of the former spring.
This based on the...
Neutrinos oscillate at different flavors while propagating in space and this is due to their mass.Any particle being massless cannot oscillate between different flavors while leptons with the mass of the electron and above are very unlikely to change their flavor. Will we able to detect a change...
Suppose I have a perfectly circular pool which is four meters in radius, two meters in depth, and filled with water. Say I drop a steel ball with a radius of five centimeters into the middle of the pool from a height of five meters above the water's surface. After three seconds, what will be the...
Suppose I prepare an experiment where I excite a single mode of oscillation of the lattice, that is something like ##u(x, t) = Ae^{i(kx-\omega t)} ## (in the classical limit). The energy corresponding to that mode should be ##E = \frac 1 2 \rho L^3 A^2 \omega^2 ##. If I equate this equation to...
Let’s say we have a boat whose longitudinal axis is the y-axis (which goes into the screen in the figure below) standing upright in a still water .
##S## is the Center of Mass of the boat and ##C## is the Center of Mass of the displaced water.On ##S## lies the force ##\mathbf W##...