Oscillations Definition and 487 Threads

Homework Statement This is an example of an Undamped Forced Oscillation where the phenomenon of Pure Resonance Occurs. Find the solution of the initial value problem: x'' + 4 x = 8 sin(2 t) , x(0)=x'(0)=0 Homework Equations The Attempt at a Solution in class we were given...

My textbook gives the equation A=Ao(e^-bt/2m) for the changing amplitude of damped oscillations. What I don't understand is where this equation comes from. Why make it to the base e? Why not make the equation A=Ao(f^T/t) where f is the factor by which it is decay and T is the period.

Homework Statement Four people, each with a mass of 71.7 kg, are in a car with a mass of 1150 kg. An earthquake strikes. The driver manages to pull of the road and stop, as the vertical oscillations of the ground surface make the car bounce up and down on its suspension springs. When the...

Homework Statement A particle of mass m is at rest at the end of a spring (force constant = k) hanging from a fixed support. At t = 0 , a constant downward force F is applied to the mass and acts for a time t_0 . Show that, after the force is removed, the displacement of the mass from...

[b]1. U(x)=U0(x/a)^1000000 Find the period for a mass m, if it has total energy E [b]2. E=U+K [b]3. dE/dt=0=v[mdv/dt+dU/dx] I am really stuck on this one, I am not sure what to do at all talked to my proffessor he says just to re-read the chapter but if I am honest I've always...

Homework Statement A string of length L is clamped at both ends, pulled up a distance h with tension T. What is the energy of the subsequent oscillations after plucking. [Hint, consider the work done against the tension in giving the string its initial deformation] Homework Equations...

Homework Statement Consider an atom of mass m bonded to the surface of a much larger immobile body by electromagnetic forces. The force binding the atom to the surface has the expression F = eacosz + bsinz + dtanz where a, b and d are constants and z is positive upwards. The...

i have asked this question before ,yet i ask again, why should we not consider the reciprocating action of the piston as simple harmonic motion? harmonic oscillations are when a particle may oscillate within unequal limits about the mean position a special case in which limits of...

I'm budgeting my time for the upcoming semester, and I've made a goal with myself to spend at the bare minimum 8 hours per week for an undergraduate course in Waves + Oscillations - with a surplus of 14 hours for a week that has an exam in it. Does this seem like a reasonable amount of time?

Homework Statement A particle of mass m moves on the inside surface of a smooth cone whose axis is vertical and whose half-angle is alpha . Find the period of small oscillations about a horizontal circular orbit a distance h above the vertex.Homework Equations Not sure. Lagrangian maybe F = ma...

A horizontal arrangement with 1 spring in between the two masses, 1 spring connecting each mass to opposite fixed points: k 3m k 8m k |----[]----[]----| I solved the eigenvalue/eigenvector problem for the dynamical matrix D where V = 1/2 D_{ij} w_i w_j and the w's are...

Homework Statement Consider two pendulums, I and II. I consists of a bob of mass 2m at the end of a rod of length L. II consists of one bob of mass m at the end of a rod of length L and another bob of mass m halfway up the road, at L/2. What is the ratio of the frequency of small...

Homework Statement The block oscillates about equilibrium for the spring. A weak frictional force of constant magnitude 2.7 N causes the oscillations to diminish slowly. The block oscillates many times and eventually comes to rest. First, show that the decrease in amplitude is the same for...

Homework Statement A 45.0-g hard boiled egg moves on the end of a spring with a force constant k = 2.50 N/m. Its initial displacement is 0.500 m. A damping force Fx = -bvx acts on the egg, and the amplitude of the motion decreases to 0.300 m in 4.0 s. Calculate the magnitude of the damping...

Hello everyone, I am having trouble understanding the concept of a limit not existing for functions like sin (1/x) when x tends to 0. The good book says that the function "does not settle on any value as we get closer to x" implying some infinite oscillation. I am having trouble visualizing...

A particle of mass m moves in one dimension subject to the potential: V(x)=(-12/x)+(x^-12) Find the equilibrium point and the frequency of small oscillations about that point. I think I've found the equilibrium point 'a', but using the formula V'(a)=0, and i got the answer a=1...

Homework Statement y'' + 6y = 2cos3t a)Determine frequency of the beats b)Determine frequency of the rapid oscillations c)Use the information from parts a) and b) to give a rough sketch of a typical solution Homework Equations The Attempt at a Solution Not sure how to do...

Homework Statement A physical pendulum consists of 4.8 m long sticks joined together as shown in Fig. 15-43. What is the pendulum's period of oscillation about a pin inserted through point A at the center of the horizontal stick...

Homework Statement A 50.0g hard-boiled egg moves on the end of a spring with force constant k = 25.0 N/m. It is released with an amplitude 0.300m. A damping force Fx = -bv acts on the egg. After it oscillates for 5.00s, the amplitude of the motion has decreased to 0.100m. Calculate the...

Homework Statement A mass-spring system oscillates with an amplitude of 3.30 cm. If the spring constant is 231 N/m and the mass is 537 g, determine the mechanical energy of the system. Homework Equations Mechanical energy is potential energy plus kinetic energy The Attempt at a...

the position of the center of the box shown is given by the equation x = 5.3 m * cos(20/sec * t) (a) What is the position of the box 2 seconds after the oscillations have started? (b) What is the amplitude of the box's oscillations? (c) What is the period of the box's oscillations...

Homework Statement I have to prove that the total energy of a spring mass system is equal to (1/2)k(delta L^2 + A^2) The spring is in three sates, equilibrium (I proved that already), maximally stretched, and maximally compressed. The spring is at equilibrium at a height h above ground level...

Homework Statement A 253 g oscillator has a speed of 89.28 cm/s when the displacement is 2.79 cm and a speed of 70.95 cm/s when the displacement is 6.56 cm. What is the oscillator's maximum speed? Homework Equations The Attempt at a Solution well, I haven't really attempted a...

I have a burning question, I was trying to find the solutions for a double mass coupled oscillation. So I found out the eigenvectors and then I arrived at this step \left( \begin{array}{c} \ddot{x_1} \\ \ddot{x_2} \end{array} \right)=\lambda \left( \begin{array}{c} x_1 \\ \ x_2 \end{array}...

Homework Statement A long, narrow bar magnet that has magnetic moment \vec{\mu} parallel to its long axis is suspended at its center as a frictionless compass needle. When placed in a region with a horizontal magnetic field \vec{B}, the needle lines up with the field. If it is displaced by a...

Hi everyone. Can you imagine a metre rule attached to a tabletop and weights are attached at the other end? The ruler will sag. The ruler is then given a push to let it oscillate. However the weights fell off when it is oscillating. So what is the effect on period and amplitude? I did...

Homework Statement The problem is: A point pendulum is being accelerated at a constant acceleration of a. Basically what's required is to find the equations of motion, the equilibrium point, and to show that the frequency of small oscillations about the e.p. is: \omega=L^{-1/2}...

Consider please that an observer is located in a plane sinusoidal and polarized e.m. wave. He erects a metalic antenna normal to the direction of propagation. A sinusoidal potential difference appears between the two ends of the antenna having the same frequency as the e.m. has. Is that a...

Homework Statement The figure below shows the x(t) curves for three experiments involving a particular spring-box system oscillating in SHM. (a) Rank the curves according to the system's angular frequency, greatest first (use only the symbols > or =, for example 1>2=3). (b) Rank the curves...

Homework Statement A particle of mass m and charge q can move along a vertical circle of radius R in the constant gravitational field of the earth. Another charge q is fixed to the lowest point of teh circle. Find the equilibrium position and the frequency of small oscillations of the...

Hello again, I am having this problem understanding Quantum Theory, when it comes to calculations and applications. I'll give you an example. When using the Bohr Sommerfeld quantization rule we use calculus in...what? Is it an oscillating particle?? That's what I can't seem to understand...

I want to convert horizontal type of oscillations to vertical oscillations. is there any existing mechanism for it? if not, what should i do.

A mass spring system with natural frequency of 1.5Hz is set up as shown: http://img300.imageshack.us/img300/7922/35809066dx2.th.jpg Can someone please explain the reasons for the following observations: When the support rod oscillates at a frequency of 0.2 Hz - oscillations are...

Which one of the following statements about an oscillating mechanical system at resonance, when it oscillates with a constant amplitude, is not correct? A The amplitude of oscillations depends on the amount of damping. B The frequency of the applied force is the same as the natural frequency...

Homework Statement Hi When you set up an LC (tank) circuit there is oscillation due to charge and discharge of capactor and storage of energy in the inductor. How do you prove that it is simple harmonic? And also how do you prove (mathematically) energy is conserved in an undamped LC...

Homework Statement Consider a particle of mass m constrained to move on the surface of a paraboloid whose equation (in cylindrical coordinates) is r^2=4az. If the particle is subject to a gravitational force, show that the frequency of small oscillations about a cirrcular orbit with radius...

Homework Statement What is the period of oscillations of a spring fixed to the ceiling at one end and set in motion by attaching a mass 10kg to the other end? The spring constant is 20 N/m. Homework Equations I used equations found in my lab book for Simple Harmonic Motion. ω=√k/m...

Homework Statement A 2.00 kg object attached to a spring moves without friction and is driven by an external force F=(3.00N) sin(2pie t). Assuming that the force constant of the spring is 20.0 N/m determine (a) the period and (b) the amplitude of the motion. Homework Equations T = 2pi...

Homework Statement http://books.google.com/books?id=uAfUQmQbzOkC&pg=RA1-PA130&lpg=RA1-PA130&dq=transverse+oscillations+spring+trisection&source=bl&ots=4tThicDJOS&sig=d7POqmkxlKMhS72_Rv7oTpMko1o Problem 5.17. Homework Equations Newton's second Law (F = ma) The Attempt at a Solution...

A 'U' shaped tube is partially filled with water. If the water inside it is disturbed from one end does it begins to move up and down. Does this motion is simple harmonic. Accelaration = force/mass = (g/h)y Time period T = 2pi/w w=(g/h)^-1/2

A ball falling through a 'V' shaped curve attains Simple Harmonic Oscillations or not. If yes give equation. Yes it is simple harmonic oscillation. But how i can prove it.

Problem related to Simple Harmonic Oscillations A test tube floats, mass 20gm is set into vertical oscillations on the surface of the water. If the external diameter of the tube is 2.5cm, show that the vertical oscillations are SHO and find period of oscillations. I found it that it attains a...

Homework Statement Marie observes damped oscillations of a glider on an air track. She observed that the amplitude decreased to 50% of its original value after 10 seconds. What is the decay constant for the motion of the glider? Homework Equations The Attempt at a Solution It...

hallo all, I was wondering if you were able to help me with the following: I am wondering about how body armor works exactly and have checked some sites, but still strugle with some questions. As for know I have the following: when a bullet hits a body, then you have injuries caused by the...

1. The problem statement, alml variables and given/known data A block of mass 2 kg is suspended from a fixed support by a spring of strength 2000 N m^-1. The block is subject to the vertical driving force 36 cos pt N. Given that the spring will yield if its extension exceeds 4 cm, find the...

Homework Statement A thin steel beam 8.0 meters long is suspended from a crane and is undergoing torsional osciallations. Two 75-kg steelworkers leap onto opposite ends of the beam, as shown in the figure (no figure given, they just jump straight towards the center of the beam). If the...

A massless sping of spring constant k=74 N/m is hanging from the ceiling. A 490g mass is hooked onto the unstretched spring and allowed to drop. Find the amplitude and the period of the resulting motion. Attempt: F= -kx x= A cos (wt) w = sqrt(k/m) t I'm trying to solve for A, but...

1) SOLVED. In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the following expression, where x is in centimeters and t is in seconds. x = (7.00 cm) cos(5t + π/8). (a) at t=0, find the position (b) velocity (c) acceleration For part a, I...

Hello: I am wondering if someone can help with the following? 1. A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position y(init) such that the spring is at its rest length. The eobject is released from...

Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut...