What is Oscillations: Definition and 517 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.
Hello. This is the figure of the problem:
First, we should determine the Lagrangian of the system. I have already completed this part without any issues. To respect everyone’s time, I won’t go into the details of how I accomplished it.
$$L=\dfrac {M+m}{2}\dot x^2+ml\dot x \dot \theta \cos...
Writing force equations for block ##m## : $$T-mr\omega^2=m\ddot{r}$$ and for block ##M## : $$Mg-T=M\ddot{r}$$ I think there are mistakes in my equations as they are leading to nowhere and morever i think force methods are really risky in this regard . It would be better to write the total energy...
I am attaching the solution given, but I am not convinced with the approach. I am also asking for some suggestions and hints if I am wrong or is there any other way around.
The thing I do not understand is the arguments from geometry they have made. How they can conclude the extension of spring...
So I proceed as:
Total time for 1 oscillation is 0.2s
$$\frac{1}{\sqrt{2}}=\sqrt{2} \sin ({\omega t_1})$$
$$\sqrt{2}=\sqrt{2} \sin ({\omega t_2})$$
Therefore
$$\omega t_2=\frac{\pi}{2}$$
$$\omega t_1=\frac{\pi}{6}$$
$$\omega ×2(t_1+t_2)=2×\left( \frac{\pi}{2}+\frac{\pi}{6}\right) $$
Since...
I was studying for a Physics Masters Entrance Exams (India) and my coaching institute basically suggested me these books:
I actually have regretted buying books without prior research in the past, so I am making sure I do my fair share of research before buying any of these or something...
Why are damped oscillation in many books written with equation
\ddot{x}+2\delta \dot{x}+\omega^2 x=0
##\delta## and ##\omega^2## are constants. Why ##2 \delta## many authors write in equation?
Perhaps that's a very dumb question, but I'm having a hard time to understand why it's possible to omit parts of the equations in solving various problems involving oscillations. Here, for example, the complete equation for acceleration is not used (the part with cosine doesn't appear) and here...
Hello! I have 2 levels, with quantum numbers ##(J=0,m_J=0)## and ##(J=1,m_J=1)## and I am a bit confused about whether I can drive Rabi oscillations between them with a fixed laser polarization. Assuming I start in the ##(J=0,m_J=0)##, I would need right-circularly polarized light to drive that...
So far I have not made much meaningful progress beyond two equations; \begin{align*}
\rho \frac{D\mathbf{u}}{Dt} = - \nabla p \implies \rho \left( \frac{\partial}{\partial t} + u \frac{\partial}{\partial r} \right)u = - \frac{\partial p}{\partial r}
\end{align*}and thermal energy:\begin{align*}...
Hi, this is a question from my textbook that I can't quite make sense of. I don't really know where even to begin, to be honest. The only thing I can think of is that the bead is at equilibrium, thus the force of gravity is equal to the pressure exerted by the gas. I don't know where the heat...
Hi,
First of all, I'm wondering if a beaded string is the right term?
I have to find the amplitude of the modes 2 and 3 for a string with 5 beads.
In my book I have $$A_n = sin(\kappa p)$$ or $$A_n = cos(\kappa p) $$ it depends if the string is fixed or not I guess. where $$\kappa = \frac{n\pi...
A disc of radius ##a## has a smaller disc of radius ##a/2## removed. The resulting object has mass ##m##:
The centre of mass ##G## is a distance ##h = \dfrac{\pi a^3 - \dfrac{3\pi a^3}{8} }{\dfrac{3\pi a^2}{4}} = \dfrac{5a}{6}## from the edge. The moment of inertia of the shape about the...
If you go beyond the harmonic approximation, phonons can not be thought as independent quasiparticles anymore and phonon-phonon interactions are taken into account. This eventually translates into the fact that phonons frequencies get renormalized ( ##\omega \rightarrow \omega^′ +i\nu ##)...
The following attempt gives the wrong answer, and I would like to know where it goes wrong.
Let ##\theta## be the angle of the ball with the vertical passing through the centre of the bowl, and ##\phi## be the angle the ball rolls through.
Let ##m## be the mass of the ball, ##r## be the radius...
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...
I did a homework problem in plasma physics recently, and got the right answer (I already submitted the assignment, that's why I didn't put this in the homework subforum), but I had to introduce a new charge density term that doesn't seem to actually exist (but it's zero at T=0). The problem was...
Hello there,
I need some advice here. I am currently studying intro physics together with calculus. I am currently on intro to oscillatory motion and waves (physics-wise) and parametric curves (calc/math-wise). I noticed that in the oscillatory motion section, I need differential equation...
I add a Figure with the problem and solution. I have difficulty with a solution to the given problem. Why ##F=-kx=Adp##, I do not understand minus sign because we are working with scalars not vectors. It is correct to say that
##\vec{F}=-kx\vec{i}##, but is not correct to say that ##F=-kx##. Can...
First of all, I found the angular frequencies for both pendulum and breathing mode which are
##\omega_p = 4.95##
##\omega_b = 7.45##
Then I found the normal mode coordinates equations:
##q_p(t) = A cos \omega_p t##
##q_b(t) = B cos \omega_b t##
And the beating frequency (I'm not sure if I...
Hi all,
I'm studying the compression spring design issue that occurred in a machine design application.
As illustrated below, spring is bouncing or oscillating after impact to a stopping surface (1 -> 2 -> 3 -> 4) and eventually stop after few bounces.
Ideal case for this application is to...
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...
I am trying to find any relation between the three parameters:
Position of the floor wrt an inertial frame f
Position of the cushion wrt floor c
Position of the man wrt cushion m
But this is really confusing, leaving me to a lot of unnecessary variables
Do you know one smart way to start?
[Moved from technical forums, so no template]
Summary:: A rod of length l and mass m, pivoted at one end, is held by a spring at its midpoint and a spring at its far end, both pulling in opposite directions. The springs have spring constant k, and at equilibrium their pull is perpendicular to...
That's a good question, i am not sure how the water in liquid state will influence in the motion, but i imagine that can not exert any torque, i would say in the first case:
Hollow sphere inertia moment: 2mr²/3 + ml²
(2mr²/3 + ml²)θ'' = -mglθ (1)
In the second case, otherwise, we will have...
Classical electromagnetic propagation evokes an electric field at right angles to a magnetic field.
Does this complementary directionality have a simpler basis in QED?
Are there any examples of an orthogonal component in other fundamental interactions?
Thanks.
I have solved it with a force approach, but would like to know how to do it via an energy approach. For starters, here is the force approach. Consider a small, approximately circular, surface element of mass ##m## such that the angle from the centre to the edge of this element is ##\alpha##...
Please note that the transformed quantities will be indicated by ##'##.
Let me give some context first.
Let us assume here that the general approximate form of the potential energy ##V## and the kinetic energy ##T## are given to be
$$V^{app} = q^T V q \tag 1$$
$$T^{app} = \dot q^T V \dot q...
I am a layman with very little experience in math and physics and recently I became curious about how to analyze dampened oscillations occurring in fluid mediums, such as those following a disturbance in a pool of water. What sort of math and physics is required to understand this phenomenon and...
Q.1. The length of a stretched string fixed at both ends has a length of l=10 cm, mass per unit length ρ= 0.01 gm/cm. If the tension ' T ' is produced by hanging a 11 kg weight at both ends of the string, then calculate,
a) The wavelength of the first two harmonics,
b) The speed of the wave...
I have general equation for undamped forced oscillations (no friction) which is:
I just wonder about,what type of motion should occur when initial conditions are both 0 (i.e v0=0 and x0=0). My intuitive expectation is that as there is no 'natural' oscillations at beginning,vibration has to be...
Since the membrane doesn't break, the wave is continuous at ##x=0## such that
##\psi_{-}(0,y,t) = \psi_{+}(0,y,t)##
##A e^{i(k \cos(\theta)x + k \sin(\theta)y - \omega t)} = A e^{i(k' \sin(\theta ') y- \omega t)}##
Which is only true when ## k' \sin(\theta ') = k \sin(\theta) ##.
From the...
This is my first thread here, so let me know if I didn't adhere to a format i was to follow. I'm in the middle of a project depicting the change that an oscillation of fluid inside a drinking straw faces depending on the viscosity of the liquid.
For reference, this is exactly the same example...
Consider the following setup:
In this, let us set the pendulum 1 into motion. The energy gets transferred through the connecting rod and the other pendulum starts oscillating due to the driving force provided by the oscillating pendulum 1. Isn't it?
So the neighbouring pendulum starts...
I calculated that the distance from the pivot to the center of mass was sqrt(2) L/4, and that the moment of inertia was 1/6mL^2+2m(L/2)^2. I simplified the moment of inertia to 2/3mL^2, and the 2mgd to sqrt(2)mgL. Cancelling out the m's and the L's, I end up with sqrt(3sqrt(2)g/2L). It says that...
Why doesn't the incline angle play a role in changing the ##m## component of this equation?
##T = 2π\sqrt{\frac{m}{k}}##
FOR QUESTION 25, PART B:
ANSWER:
Let's try inputting a solution of the following form into the two-dimensional wave equation: $$ \psi(x, y, t) = X(x)Y(y)T(t) $$
Solving using the method of separation of variables yields
$$ \frac {v^2} {X(x)} \frac {\partial^2 X(x)} {\partial x^2} + \frac {v^2} {Y(y)} \frac {\partial^2 Y(y)}...
Hi,
Given a mechanic-problem, I've linearised a system of two differential equations, which the origin was Lagrange-equations.
The system looks like this;
$$ 5r \ddot{\theta} + r \ddot{\phi} + 4g \theta = 0´ \\ 3r \ddot{\theta} + 2r \ddot{\phi} + 3g \phi = 0 $$
$$ $$
And I shall find the...
So I'm working on this home assignment that has numerous segments. Firstly, I was asked to find the equilibrium distance between two particles in a potential well described by U(r).
I did that by setting U'(r) = 0 and came out with r_equilibrium = 2^(1/6)*a.
Now, I'm being asked to find the...
I've generally solved introductory second order differential equations the 'normal' way; that is, using the auxiliary equation, and if it is inhomogeneous looking at the complementary function as well, and so on.
I know that sometimes it can be helpful to propose an ansatz and substitute it...
Hi PF!
I'm looking at a sessile drop of water in ambient air. The drop is plucked lightly, inducing surface oscillations. The fundamental frequencies ##\lambda_i## can be computed from spectral theory, and output complex values, say ##\lambda_1 = 2+7i##.
Now, I simulate the experiment via CFD...
For a harmonic oscillator with a restoring force with F= -mω2x, I get that the solution for the x-component happens at x=exp(±iωt). But why is it that you can generalise the solution to x= Ccosωt+Dsin(ωt)? Where does the sine term come from because when I use Euler's formula, the only real part...
Continuing on from the summary, the chapter has given a graphed example. We are shown a regular cosine wave with phase angle 0 and another with phase angle (-Pi/4) in order to illustrate that the second curve is shifted rightward to the regular cosine curve because of the negative value. Now, my...
This is the image provided with the problem, the values given include:
d= 4.00 m, the mass of block one=0.200 kg, speed of block one=8.00 m/s, the period of oscillations for block two without friction=0.140 s, and the spring constant= 1208.5 N/m.
I know how to solve the oscillations if block...
Hey, I solved a problem about a double pendulum and got 2 euler-lagrange equations:
1) x''+y''+g/r*x=0
2) x''+y'' +g/r*y=0 (where x is actually a tetha and y=phi)
the '' stand for the 2nd derivation after t, so you can see the basic harmonic oscillator equation with a term x'' or y'' that...
Summary: I have been trying to understand the abstract and introduction to the paper
https://arxiv.org/pdf/astro-ph/0501171.pdf
DETECTION OF THE BARYON ACOUSTIC PEAK IN THE LARGE-SCALE CORRELATION FUNCTION OF SDSS LUMINOUS RED GALAXIES.
I made an effort to find in the paper the answers to...
I'm trying to solve the following set of equations across several discrete increments. These aren't the exact equations I'm using, but they're a simplified version with the same general structure...it's basically a set of equations describing a transfer rate along a fixed length, where "Z" is...
I first found the equilibrium points taking the derivative of the potential. ##U'(x)=U_0 a\sin(ax)##, and the equilibrum is when the derivative is 0, so ##U_0 a\sin(ax)=0## so ##x=0## or ##x=\pi/a##. Taking the second derivative ##U''(x)=U_0a^2 \cos(ax)## I find that ##x=0## is a minimum point...