Oscillation Definition and 740 Threads

Hi there! I have this problem: How to calculate the frequency of the oscillations of an electron from its equilibrium point in this potential: V(z)=k/(2ɛ)*[sqrt(z^2 - 9R^2) - sqrt(z^2 - r^2)]*sgn(z)

Homework Statement A 100 g ball is attached to a spring with spring constant 2.5 N/m oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x = -5.0 cm. What is the amplitude of the oscillation? Homework Equations x = Acos(ωt +φ ) V= -ωAcos(ωt +φ ) The...

Homework Statement A 2.0 m long string vibrates at its second harmonic frequency with a maximum amplitude of 2.0cm. One end of the string is at x = 0cm. Find the oscillation amplitude at x = 10,20,30,40, and 50cm. Homework Equations A(x) = 2asin(kx) k= 2pi/wavelength The Attempt at...

Homework Statement An object in SHM oscillates with a period of 4.0 s and an amplitude of 10 cm. How long does the object to move from x = 0.0 cm to x = 6.0 cm? Homework Equations x(t) = Acos(ωt +φ ) The Attempt at a Solution ω = π/2 Acosφ = 0 ⇒φ = ±π/2 Since object is moving...

I am not sure that I understand what damped harmonic oscillation is different from simple harmonic oscillation, can someone please explain that to me? I read wikipedia and still doesn't get it...

Homework Statement A 200 g ball attached to a spring with spring constant 2.50 N/m oscillates horizontally on a frictionless table. Its velocity is 18.0 cm/s when x = -5.00 cm. A. What is the amplitude of oscillation? B. What is the speed of the ball when x = 3.00 cm? Homework Equations A...

Homework Statement This problem was presented as part of a lab write up. In the lab we were studying damped oscillations. We were asked to determine the mass indirectly based on values that we measured then compare it to the actual masses. We found that the calculated masses were much greater...

I don't really understand why neutrino oscillation occurs so I looked it up on wikipedia: http://en.wikipedia.org/wiki/Neutrino_oscillation I went to the "Theory, graphically" section and it gives quite a good explanation. However, there are a few details I don't get. It says: "This...

I think I solved the problem but tell me if I made any errors Homework Statement A tray of mass m, when suspended from a spring attached to the ceiling, stretches the spring by a distance Δx. A glob of peanut butter with mass M is dropped from a height h onto the tray, which is at rest...

Homework Statement A 2 kg object attached to a spring moves without friction and is driven by an external force given by F = (3.00N)sin(2\pit). The force constant of the spring is 20.0N/m. Find the amplitude of the motion. Homework Equations I am not sure but I am trying to use: A =...

Homework Statement A particle P of mass m moves on the x-axis under the force field with potential energy V=V0(x/b)4, where V0 and b are positive constants. Show that any motion of P consists of a periodic oscillation with centre at the origin. Show further that, when oscillation has amplitude...

Homework Statement I'm lost at how to derive the probability of a neutrino species surviving an oscillation. After performing calculations, I can't seem to get it into the nice tidy form 1-\sin^{2}2\theta\sin^{2}\left(\frac{\Delta m^{2}t}{4p}\right) Homework Equations Whatev...

I was wondering if someone could help me with Goldstein's equation 6.3 (3rd Edition). It is the chapter of oscillations and all that he has done in the equation is to expand it in the form of a Taylor series. I can't seem to get how all those ni's come to get there.

Homework Statement A simple pendulum of mass m and lenghth l is suspended in a car traveling with a constant speed v around a circle of radius r.If the pendulum undergoes small oscillations about its equilibrium position, what will be the frequency of the oscillations?? Homework Equations...

Hey all, I am having trouble determing how to get the max amplitude of an underdamped oscillation. Can someone please tell me where do I start form.

1. A 0.50 Kilogram block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. The total mechanical energy 0.12 Joules. What is the greatest speed of the block. If somebody could just point me in the right direction, I'd appreciate it...

Homework Statement A body of uniform cross-sectional area A = 1 cm^2 and of mass density p = 0.8 g/cm^3 floats in a liquid of density p0 = 1 g/cm^3 and at equilibrium displaces a volume V = 0.8 cm^3. Show that the period of small oscillations about the equilibrium position is given by: T...

Homework Statement A mass m at the end of a spring oscillates with a frequency of 0.83 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of me? Homework Equations w = 2 pi f w^2 = k / m The Attempt at a Solution m = .74725 kg I'll...

A plate of mass m is supported by a light spring fixed vertically on the ground. A plasticine is dropped gently onto the block when it is are the highest position. Which of the following statements is/are correct? 1) The amplitude of the oscillation would increase since the equilibrium position...

oscillation question -- vibration topic Book is asking me to prove that ξ = 1 corresponds with the smallest value of c such that no oscillation occurs. Says let λ = -b (b is a positive number) and that's all I'm given. I'm not even sure I understand how you can tell there is no...

Homework Statement A person places a 2.2kg truck against a horizontal spring (k=2300N/m) on a frictionless horizontal surface. The spring is compressed 15cm and released. a) How much energy is stored in the spring just before the truck is released? b) What is the velocity of the truck...

Homework Statement A model to describe the vibrations of atoms in a solid is to assume that the atoms are isotropic harmonic oscillators and that the vibrations are independent of the vibrations of the other atoms. We use this model to describe the entropy and heat capacity of Bohrium (B). The...

Homework Statement Determine the period of oscillations of a simple pendulum ( a particle of mass m suspended by a string of length l in a gravitational field) as a function of the amplitude of oscillations. Homework Equations T(E) = \sqrt(2m) \int^{x_2(E)}_{x_1(E)}\frac{dx}{\sqrt(E-U(x)}...

A 780-g mass is attached to a vertical spring and lowered slowly until the mass rests at its equilibrium position 30 cm below the original length of the spring. It is then set into simple harmonic motion. (a) What is the frequency and period of the oscillation? (b) What is the maximum...

[SOLVED] Undamped, Forced Oscillation Homework Statement Damping is negligible for a 0.133 kg mass hanging from a light 6.80 N/m spring. The system is driven by a force oscillating with an amplitude of 1.34 N. At what frequency will the force make the mass vibrate with an amplitude of 0.445 m...

Homework Statement A liquid is placed in a U-Shaped tube. Initially both are at the same level. Total length of liquid is L. But later one side is displaced from equilibrium by X.(Difference of both sides is 2x now). Show that the water will oscillate harmonically in the form of a=-w squared...

[SOLVED] More Spring oscillation Homework Statement A 2.20 kg mass is attached to a spring and placed on a horizontal, smooth surface. A horizontal force of 17.6 N is required to hold the mass at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The mass...

Hello, Ive been working on some oscillation problems and i got a couple of them correct (im suspecting flukes) but i can't get past this one: The position of a mass that is oscillating on a spring is given by (17.5cm)cos[(11.0s^-1)t]. What is the speed of the mass when t = 0.820 s? I...

A particle oscillates back and forth in a frictionless bowl whose height is given by h(x) = 0.22x2 where h and x are meters. (a) Show graphically how the potential and kinetic energies of the particle vary with x. (b) Where does the particle have maximum kinetic energy? (c) If the maximum...

Part1-A tunnel is bored through the center of a planet, as shown in the figure. (This drawing is NOT to scale and the size of the tunnel is greatly exaggerated.) Assume that the planet is a homogenous sphere with a total mass M = 3.5x 1024 kg and a radius R = 6600 km. A package of mass m = 7.5...

Homework Statement A sinusoidally varying driving force is applied to a damped harmonic oscillator of force constant k and mass m. If the damping constant has a value b_1, the amplitude is A_1 when the driving angular frequency equals sqrt (k/m). In terms of A_1, what is the amplitude for...

[SOLVED] Dampened Harmonic Motion Homework Statement A mass M is suspended from a spring and oscillates with a period of 0.900 s. Each complete oscillation results in an amplitude reduction of a factor of 0.985 due to a small velocity dependent frictional effect. Calculate the time it takes...

[SOLVED] oscillation frequency of circuit Homework Statement An L-C circuit containing an 83.0 \rm mH inductor and a 1.50 \rm nF capacitor oscillates with a maximum current of 0.800 A. Calculate the oscillation frequency of the circuit. Homework Equations \omega =...

The question is "The magnitude of the gravitational acceleration inside Earth is given approximately by g(r) = g_0(r/R_E), where g_0 is the surface value, r is the distance from Earth's center, and R_E is Earth's radius; the acceleration is directed toward Earth's center. Suppose a narrow...

Working through my lecture summaries, I have been given that Q (the quality factor) =\frac{2\pi}{(\Delta E/E)cycle} and accepted this as a statement, taking \((\Delta E/E)cycle} to mean the 'energy loss per cycle'. The notes carry on to say 'The frequency \widetilde{\omega} of...

Homework Statement Two identical springs have attached mass M1 on the one and mass m2 on the other. We found that the psrings with mass m1 osciallates with a 2/5 frequency of the other spring.. Find the ratio of the mass of spring B to that of spring A ( M2/M1) Can someone work this out...

Hi everybody! I have a big question for you, I have been staring me blind on this problem I got. And wonder if someof you could help mee with it? the guestion is this: "Find the time dependent oscillation u(t) for time t>0 for a damped system with one degree of freedome where c=50 kg/s...

we know in bloch oscillation, the wavefunction of an electron returns to its initial state after a period, but up to a phase. my question is, can this phase be nontrivial?

We want to support a thin hoop by a horizontal nail and have the hoop make one complete small-angle oscillation each 2.0s . What must the hoop's radius be (in meters) ? and An object is undergoing SHM with period 0.260 s and amplitude 5.55 cm. At t=0 the object is instantaneously at...

[SOLVED] Forced Oscillation Q Homework Statement A 2.00kg object attatched to a spring moves without friction and is driven by an external force given by F= (3.00N)sin(2 \pi t) The force constant of the spring is 20N/m. Determine a) period b) amplitude of motion Homework...

Homework Statement A physical pendulum consists of a meter stick that is pivoted at a small hole drilled through the stick a distance d from the 50 cm mark. The period of oscillation is 2.5 s. Find d Homework Equations T=2PI*sqrt(I/mgh) I(com)=(1/2)mL^2 parallel axis theorem...

1. The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12-degree to the verticle. (a) With what frequency does it vibrate? Assume SHM. b) What is the pendulum bob's speed when it passes through the lowest point of the swing? c)...

Homework Statement A damped oscillator of mass m=1,6 kg and spring constant s=20N/m has a damped frequency of \omega' that is 99% of the undamped frequency \omega. As found out by me: The damping constant b is 0.796 kg/s. Q of the system is 7.1066 kg^-1. Are the units here right? The...

Homework Statement Show that the local maximum or minimum for the displacement of an underdamped oscillation does not occur halfway between the times at which the mass passes its equilibrium point. Homework Equations x = e^{-\frac{ct}{2m}}(A cos(wt) + B sin(wt)) x = K e^{-\frac{ct}{2m}} sin(wt...

What causes the Pacific decadal oscillation in which a large part of the pacific ocean gets hotter than normal - this effect superimposes itself on El Nino.Is the pacific decadal oscillation linked to El Nino - does one cause the other?

[SOLVED] Spring Oscillation Problem! 1. A 2.0 kg mass hangs at rest from a harmonic spring with a spring constant of 500 N/m inside an elevator that is stationary. a) by how much is the spring stretched b) suppose that the elevator is rising with a constant upward accel of 1/3 g. By how...

[SOLVED] Angular momentum and oscillation of disk A large solid disk of mass M and radius R is mounted on a fixed axis through its center using ideal bearings. A small projectile of mass m_1 traveling with velocity v_1 collides tangentially to the slight extension and sticks to the larger disk...

1. Homework Statement [/b] Let Z(t)=(3/4)Sin(2π/3t) be the equation for a SHO in the Z diection about z=0. 1. what are the amplitude, phase, frequency, angular frequency and period of this SHO? 2. what is the maximum velocity? what is the maximum acceleration? 3. when Z= 3/4, what...

1. Homework Statement A winch cable has a cross sectional area of 1.5 cm^2 and a length of 2.5 m. Young's modulus for the cable is 150 GN/m^2. A 950-kg engine block is hung from the end of the cable. (a) By what length does the cable stretch? (b) If we treat the cable as a piece of string...

Homework Statement A compact car has a mass of 1300kg. Assume that the care has one spring on each wheel, that the springs are identical, and that the mass is equally distributed over the four springs. a.) What is the spring constant of each spring if the empty car bounces up and down 1.4...