Vibrations Definition and 236 Threads

Homework Statement Consider the van del Pol equation [tex]\ddot{u}-ε(1-u^2)\dot{u}+u=0[\tex] Determine the limit cycle for ε=1 using the incremental harmonic balance method. Validate the result using numerical integration (e.g., Runge Kutta). Homework Equations It's incremental...

Homework Statement We are deriving the PDE that models a hanging chain of Length L. The x-axis is placed vertically. Positive direction points upwards. The fixed end of the chain is at x=L. Let u(x,t) denote the deflection of the chain. We assume the deflection is in the x,u plane. Let...

Here is my problem verbatim. A mass weighing 100g stretches a spring 5cm. If the mass is set in motion from its equilibrium position with a downward velocity of 10cm/s, and if there is no damping, determine the position \(u\) of the mass at any time \(t\). When does the mass first return to its...

The title may be incorrect, I named this after the section of my book in which this is located. My problem is as follows. Determine \(\omega_0\), R, and \(\delta\) so as to write the given expression in the form \(u=R\cos(\omega_0 t-\delta)\) \(\color{blue}{u=4\cos(3t)-2\sin(3t)},~\text{My...

Homework Statement A mass of 0.3kg is suspended from a spring of stiffness 200Nm-1. If the mass is displaced by 10mm from its equalibrium position and released, for the resulting vibration calculate: The maximum velocity of the mass during the vibration. Homework Equations v =...

Hi, I'm trying to calculate the vibrational energy of a water droplet for a given vibrational amplitude. Rayleigh wrote about this in Proc. R. Soc. Lond., volume 29, 1879, "On the Capillary Phenomena of Jets", Appendix II, but he makes some simplifications (as I understand it) and I also...

I've heard light compared to vibrations under the earth. The "waves" between the tectonic plates are simply a 'state', or 'action', i.e, the action of millions of atoms "bumping" into each other with their opposite charges (all the valence electrons repel other electrons). From my...

Hi, What is the material which would develop powerful vibration for a sustained period when they are stroked with another material(may be the same or a different material).

Homework Statement From A.P. French, question 3-10. I'm having trouble decoding part b. /Do not solve/ please help me find what it is asking. ------- A metal rod, 0.5m long, has a rectangular cross section of 2mm2. (a) This question provided me with information to calculate young's modulus...

Homework Statement Suppose the motion of a spring has natural frequency 1/2 and is undamped. If the weight attached is 32lb, write a differential equation describing the motion. Homework Equations my''+ky=F_ocosωt 32y"+8y=? ω_o= (k/m)^.5 The Attempt at a Solution → .5=(k/32)^.5 → k=8...

what exactly are residual modes of vibrations? I have come across this terminology in various fem solvers like ansys and pam crash.

Author: A.P French Title: Vibrations and Waves Amazon Link: https://www.amazon.com/dp/0748744479/?tag=pfamazon01-20 Prerequisities: Level:

Hi, I'm reproducing a measurement of vibrations and I would like your help with a certain question I have. I have a rectangular plate supported by two rods and I want to measure it's fundamental flexural vibration frecuency, among other things. As a base I have a report of such a measurement...

Is it true that strings can vibrate in certain manners in which they cause a "ripple effect" in spacetime, affecting the topology of the higher dimensions, causing these different timelines to occur in which you have changes so minor as to electrons a plank's unit to the right, or so drastic as...

A tuning fork vibrates 235 times in 3.1 seconds with an amplitude of 0.59mm. Determine.. i) its frequency ii) its period iii) the distance the end of one of the fork tines travels in one second for i) The answer I got is f=75.81Hz ii) The answer I got is 0.13s iii) ?

Homework Statement a)x=cos2ωt, y=sin2ωt b)x=cos2ωt, y=cos(2ωt-∏/4) c)x=cos2ωt, y=cosωt draw the graphs of Simple Harmonic Motions.Homework Equations parametric and complex harmonic motion equation is needed.The Attempt at a Solution No attempt to solution.I can't do anything,because I can't...

Hey everybody, I'm trying to figure out what the vibration modes of a circular membrane would look like if we put some sound through it. As you may know does a circular membrane with clamped edges at radius a behave according to the wave equation. The general solution thereof has the form...

hello all.there is a electric hoist cradle(Temporary personnel lifting;make fixator) which one of our contractor uses to clean the outside glasses of a high rise building.the cables are suspended up at the top railing with fasteners and then the electric motor escalates the cradle for use.the...

Hi, I'm triyng to model electric drive with a load in simulink. The load is a thin plate of a known dimensions, axis of rotation is passes through the center of mass parallel to the lower and upper edges. The motor is direct drive and moves the plate on a known angle with a known...

I was wondering what the common methods for solving such a system are: 2 m \ddot{x} - m l \ddot{θ} θ + k x = 0 m l^{2} \ddot{θ} - m l \ddot{x} θ + m g l θ = 0

I know that accelerating electrons in a solid are responsible for the emission, absorption and reflection of light. However, what role do the lattice vibrations play? These oscillating atoms are charge distributions and should emit radiation too, right? As far as I can remember, the...

And vehicles on the ground as well, in particular heavy ones like trucks. How do the ground and windows to vibrate?

If forced vibrations from one object to another were strong enough, would the second object start adjusting its shape to match the first?

hi guys, I need a vibration book to download... any1 to help please?

According to quantum mechanics, every particle has an uncertainty of position and momentum. Particles have quantum vibrations. So is it possible for all the atoms in an object to vibrate at the same time in the same direction making the object as a whole move? If so, what kind of energy would...

Homework Statement FYI - I don't have any knowledge on the mechanical aspects of electric motors. you're given a 400 hp electric motor that needs to run at varying rpms. The armature is 1200 lbs and is 800mm long with a diameter of 500 mm. the air gap that exists is 2.5 mm. At 800 rpm the air...

Good evening, I am unsure as to whether or not I am posting this question in the apropraite section of the this forum and apologize if I am not. With that said I will let you in on the question that I have for you tonight. I am currently a fourth year undergraduate student pursuing a...

A stretched string of mass m, length L, and tension T is driven by two sources, one at each end. The sources both have the same frequency  and amplitude A, but are exactly 180 degrees out of phase with respect to one another. (Each end is an antinode). What is the smallest normal mode...

I know that particles in a solid are not fixed. They are constantly vibrating about their mean position. That is because of their kinetic energy. I was imagining a situation, lets say solid moves towards left of it's mean position. then the inter-molecular forces of attraction on the left...

Homework Statement what distance x from the axis of variation O should be 1 kg slider, the system oscillations period is 0.9 s? T=0.9 s; the spring stiffness k=75 N/m; slider mass m=1 kg; beam mass m=3 kg; Homework Equations I\varphi(over letter "..")+k\varphi=0 \varphi(over...

Hi, Please can anyone help me here? Consider the link below; http://online.physics.uiuc.edu/courses/phys193/Lecture_Notes/P193_Lect4_Ch4_Part2.pdf I'm just trying to qualitatively undestand the pictures in the above link. Consider Page 2 of 18 Now, consider figure 3.6...

Hi, I'm trying to understand vibrations and specifically what happens in the natural modes of frequency.. 1. It seems that the harmonic nature of solution(with Acos(wt)...where A is the amplitude) applies only in the natural mode of vibration...and so the system will have a defined mode...

Homework Statement A 1.50-kg ball and a 2.00-kg ball are glued together with the lighter below the heavier one. The upper ball is attached to a vertical ideal spring of force constant 165 N/m, and the system is vibrating vertically with an amplitude of 15.0 cm. the glue connecting them breaks...

Homework Statement Find the general solution for the differential equation Homework Equations y'' + 16y = tan(4t) The Attempt at a Solution I get C1cos(4t) + C2sin(4t) = 0 for my homogeneous equation. I did the usual method of undetermined coefficients (I think I took all of the...

Homework Statement A mass moves under a potential V (x) = V0 cosh (x / x0 ) , where V0 and x0 are constants. a) Make a sketch of V(x) b) Find the position of stable equilibrium c)Show that the frequency of small vibrations about this point is the same as it would be if the mass was in...

I'm not sure whether to put this in Earth or Astrophysics. How far would these sound vibrations/waves travel? Do they just stay within the Earth, or is it possible for them to travel through space; and if so, how or why or is it possible for these vibrations to attract asteroids?

in a spring mass damper system subjected to a periodic force. the response of the system only depends on the force and the restoring forces caused due to the spring is ignored because the damper is assumed to have taken care of it. now it's here that my confusion originates. in a damped free...

hi this is word21. I have a question to anyone who can help in any way.is there a mathmatic form. that is best to use to asign integrals to musical scales as in a=x number

I am trying to design a small isolator system for a vehicle payload. I want to run it through a sine-on-random and a random-on-random input to try and optimize the design, but I am having trouble finding exactly what to use for the input functions. I assume it is more involved than typing...

Homework Statement anyone have any suggestions for devices which generate vertical vibrations, preferably of variable amplitude (say, up to a cm or so) and of variable frequency (around 10hz) which can be used to vibrate a container full of, say, sand? Homework Equations umm... The...

Homework Statement this is a design course project, and I am trying to replicate a music box but with my own choice of music. the concept is the same, a steel comb, being plucked at by protrusions from a rotating cylinder. ok, so the vibrations of each comb tooth are related to the length of...

Homework Statement An exhaust fan mass 90 kg operates at 1100 rpm and is supported by an UNDAMPED vibration isolator i.e a spring that has a stiffness of 220 kN. If the harmonic force produced by the fan has a magnitude of 12 kN determine: a) The transmitted force through the isolator to...

Hi people can anyone help me? I need to know how much energy it takes to vibrate a mass at a frequency and speed. How much energy is there in a mass of ex. 100Kg at 10Hz and a speed of 10mm/s ? Tangs!

Homework Statement I need to calculate the frequency, angular frequency and period of sinusoidal vibrations in simple harmonic motion. The acceleration amplitude is 10g (98.1m s-2) and the vibration amplitude is 2cmHomework Equations The equation I have for frequency is f=(√(a/A))/2*pi where a...

Hi, Can anybody recommend an advanced book concerning mechanical vibrations? I'm especially interested in vibrations of a spehere, hemispehere and bell. Thank you!

Homework Statement A spring and dashpot system is to be designed for a 32lb weight so that the overall system is critically damped. (a) How must the damping constant γ and spring constant k be related? (b) Assume the system is to be designed so that the mass, when given an initial velocity of...

Homework Statement A piston of mass 4.53(kg) is traveling in a tube with a velocity of 15.24(m/s). It engages a spring of stiffness 350 (N/cm) and a damper with a coefficient of 1.75 (N.s/cm) What is the maximum displacement of the piston and how long does it take to reach this point...

Homework Statement In his presentation of the de Broglie wavelength and the wave/particle duality, my quantum prof. has an exercise: "Find the de Broglie wavelength of a molecular vibration. Do quantum or classical laws apply?" Homework Equations wavelength = h/(momentum) ...

Hello. So today I came up with an idea that since light if vibration as well as sound, could sound emit light? I know through sonoluminescence light is emitted from water using the three sides of space and vibration. I just thought it might be cool to play a keyboard or something and have...

Hi I have a few questions i need some help on. Homework Statement The position of a particle is given by the expression x=(4.00m) cos(3.00\pit+\pi), where x is in meters and t in seconds. Determine (a) the frequency and period of the motion. Homework Equations f=\frac{1}{T}...