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.
I understand that
K_l = \frac{d\bar{s} + s\bar{d}}{\sqrt{2}}
K_s = \frac{d\bar{s} - s\bar{d}}{\sqrt{2}}
This happens because K_0 is oscillating into its own antiparticle.
My question is, why the same is not applicable to the neutrinos? They do oscillate. So instead of ‘pure’ e, mu, tau...
Homework Statement
Consider a system of one generalized coordinate theta, having the following Lagrangian equation of motion:
r and b are constants
m is mass
(1/3)mb^{2}\ddot{\theta} = r(r+b)\theta + r^{2}\theta^{3} + gr\theta
And this potential energy (if it matters):
U = mg(r+b)...
Homework Statement
An oscillator with a mass of 520 g and a period of 0.500 s has an amplitude that decreases by 1.00% during each complete oscillation.
PART A : If the initial amplitude is 10.2cm , what will be the amplitude after 43.0 oscillations?
PART B: At what time will the energy be...
Homework Statement
The interior of a thin spherical shell of mass M and radius R is completely filled with water and hangs from a ceiling on a light thread. The distance from the sphere's center to the hanging point is L, and the mass of water is m. Determine the change in the frequency of...
Question Details:
A 1.44 kg monkey wrench is pivoted at one end and allowed to swing as a physical pendulum. The period of its motion is 0.860 s, and the pivot is 0.290 m from the center of mass of the wrench.
(a) What is the moment of inertia of the wrench?
0.0767 kgm2
If the wrench is...
The scale of a spring balance reading from zero to 180 N is 7.00 cm long. A fish suspended from the balance is observed to oscillate vertically at 2.50 Hz. What is the mass of the fish? Neglect the mass of the spring.
________ kg
Attempt
k =(180-0)/(7-0) = 25.714 N/m
frequency =...
Homework Statement
A mass of 1.5 kg oscillates vertically at the end of a lightweight spring. The spring has a spring constant of 145 Newtons per meter. The amplitude of the motion is 8.00 cm. From this data, complete the table below.
I have to find velocity, acceleration, elastic...
Homework Statement
http://img51.imageshack.us/img51/853/39983853.jpg
2. The attempt at a solution
Q3.1
I get the general solution as
x(t) = Ae^{3t}+Be^{-t} + cost - 2sint .
Q3.2
Letting
y=\dot{x}
and using the general solution, we get...
http://fatcat.ftj.agh.edu.pl/~i7matras/hej.jpg
Both masses are in point.
I need to count displacement x(t) but I don't know how to write derivative equations? Could someone help? Or at least give me a tip?
Homework Statement
A 111g ball is tied to a string. It is pulled to an angle of 4.40 Degrees and released to swing as a pendulum. A student with a stopwatch finds that 17 oscillations take 19.0s.
How long is the string?
Homework Equations
T = 2π√(L/g)
The Attempt at a Solution
Period T =...
Homework Statement
The graph of displacement versus time for a small mass at the end of a spring is shown. At t = 0, x = 0.43 cm. (a) If m = 14.3 g, find the spring constant, k. (b) Write the equation for displacement x as a function of time.
Homework Equations
f = (1/2pi) * SQRT...
1. A uniform coin with radius R is pivoted at a point that is a distance d from its center. The coin is free to swing back and forth in the vertical plane defined by the plane of the coin. For what value of d is the frequency of small oscillations largest?
2. V(x)\equivpotential energy...
Homework Statement
Determine the equations governing the oscillations of a metronome.
The Attempt at a Solution
I believe that it has something to do with simple harmonic motion but I'm not sure where to start. Any help would be great.
Homework Statement
Suppose a particle of mass 0.240 kg acted on by a spring undergoes simple harmonic
motion. We observe that the particle oscillates between x = 0.200 m and x = - 0.200 m
and that the period of the oscillation is 1.20 s. At time t = 0, the particle is at x = 0 and
has...
Homework Statement
The two blocks in the figure oscillate on a frictionless surface with a period of 1.5 s. The upper block just begins to slip when the amplitude is increased to 36 cm.
What is the coefficient of static friction between the two blocks?
Homework Equations
The...
Homework Statement
Find the frequency of oscillations of a particle (mass m) which is free to move along the parabola y= -ax^2 + 2ax - a, and is attached to an ideal spring whose other end is fixed at (1,l) A force F is required to extend the spring to length l. a can be any real number...
Hello,
I am currently working on a lab in which we are studying the behaviour of chain of metal bars attached together with nylon wire in such a way as to to mimic the ability of solids or liquids to transmit a wave.
After studying the normal modes of the system as well as the quality...
Homework Statement
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 the rod. Find the frequency of small...
Homework Statement
An oscillator with a mass of 600 g and a period of 1.20 s has an amplitude that decreases by 2.50% during each complete oscillation. If the initial amplitude is 6.40 cm, what will be the amplitude after 50.0 oscillations?
Homework Equations
How do I approach this...
Homework Statement
Please calculate the units for the spring constant k in two fashions. First, from
Hooke’s Law (eqn. 5 in lab manual), and then from the period equation for a spring
(eqn. 3). Please show that these units are compatible (i.e. mean the same thing).Homework Equations...
Greetings,
I have been thinking as everything being particles and only appearing wavelike in double-slit experiments because they were in superposition.
Now I am reading that they are really only waves. Waves in what medium?
Thanks
the formula for damped oscillations is given as x = Ae^(-bt/2m) cos(ωt+Φ)
so why is the amplitude as a function of time given as only the first part?
meaning only A(t) = Ae^(-bt/2m)
it "ignores" the 2nd term which is the oscillating cosine term. which still encompass a time t value...
I have a question about vertical oscillations. If a vertical spring, fixed at one end with a mass attached to the other and held so that the spring is not stretched.. is then released, will the amplitude of the subsequent oscillations be the distance between the new equilibrium point (of mass...
A point of mass slides without friction on a horizontal table at one end of a massless spring of natural length a and spring const k as shown in the figure below. The other end of the spring is attached to the table so it can rotate freely without friction. The spring is driven by a motor...
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...