# Oscillations Definition and 37 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.

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1. ### Omission of parts of equations in solving oscillation questions

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...
2. ### Derive the period of a Ball rolling in a Bowl

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...
3. ### Real and Complex representations of an oscillation equation

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...
4. ### Waves and vibrations on a string

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...
5. ### Wave behavior across two semi-infinite membranes with a special boundary

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...
6. ### B Do fluid oscillation characteristics depend on the viscosity of a fluid?

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...
7. ### Normal modes of a rectangular elastic membrane

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)}...
8. ### B Shifting of a Cosine Curve with negative phase angle values

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...
9. ### Natural angular frequency

Homework Statement The suspension of a modified baby bouncer is modeled by a model spring AP with stiffness k1 and a model damper BP with damping coefficient r. The seat is tethered to the ground, and this tether is modeled by a second model spring PC with stiffness k2. The bouncer is...
10. ### Spring with oscillating support (Goldstein problem 11.2)

Homework Statement A point mass m hangs at one end of a vertically hung hooke-like spring of force constant k. The other end of the spring is oscillated up and down according to ##z=a\cos(w_1t)##. By treating a as a small quantity, obtain a first-order solution to the motion of m in time...
11. ### Simple Harmonic Motion: why sin(wt) instead of sin(t)?

Hello, I have recently been introduced to the topic of simple harmonic motion for the first time (I'm currently an A-level physics student). I feel that I have understood the fundamental ideas behind SHM very well. However, I have one question which has been bugging me and I can't seem to find a...
12. ### Find an Expression for the Frequency - Pendulum

Homework Statement [/B] A solid sphere of mass M and radius R is suspended from a thin rod. The sphere can swing back and forth at the bottom of the rod. Find an expression for the frequency of small angle oscillations. Homework Equations f = 1/2(pi) sqrt(MgR/I) I for a solid sphere 2/5MR^2...
13. ### Spoke card oscillations

Homework Statement A thin card produces a musical note when it is held lightly against the spokes of a rotating wheel. If the wheel has 32 spokes, how quickly must it rotate, in revolutions per minute, in order to produce the A above middle C (i.e. 440 Hz)? Homework Equations ω=2πƒ; ƒ=1/T...
14. ### Small oscillations and a time dependent electric field

Homework Statement [/B] Here's the problem from the homework. I've called the initial positions in order as 0, l, and 2l. Homework Equations The most important equation here would have to be |V - w2*M| = 0, where V is the matrix detailing the potential of the system and M as the "masses" of...
15. ### Complex Solutions to Oscillations

Homework Statement Homework Equations The Attempt at a Solution I tried differentiating both sides of 3 and re-arranging it such that it started to look like equation 2, however i got stuck with 2 first order terms z' and couldn't find a way to manipulate it into a function z. I then...
16. ### Damped oscillation of a car on a road: velocity calculation

Homework Statement The car circulates on a section of road whose profile can be approximated by a sinusoidal curve with the wavelength of 5.0 m. The mass of the car is 600.0 kg, and each wheel is equipped with a constant spring k = 5000 Nm-1 and a damper with constant b = 450 Nm-1s. Calculate...
17. ### Resistance of an oscillating system

Homework Statement [/B] Homework Equations ##F = -kx = m\ddot{x} ## ## f = \frac{2\pi}{\omega}## ## \omega = \sqrt{\frac{k}{m}} ## ##\ddot{x} + \gamma \dot{x}+\omega_o^2x = 0 ## ##\gamma = \frac{b}{m}## The Attempt at a Solution I'm stuck on part c of this question. Using the above...
18. ### Spring set makes up a traveling wave

Homework Statement Twelve identical mass-spring combos are lined up and set to oscillation. Two pictures of the same system taken at different times are shown. The crest-to-crest distance is 8.0 cm, and the maximum displacement of all the masses is 1.5 cm. 1) Explain how you can tell that a...
19. ### Resonance in forced oscillations

Homework Statement Consider the differential equation: mx'' + cx' + kx = F(t) Assume that F(t) = F_0 cos(ωt). Find the possible choices of m, c, k, F_0, ω so that resonance is possible. Homework Equations The Attempt at a Solution I know how to deal with such problem when there is no damping...
20. ### B For oscillations, why do we use angles in waves and oscillat

For example, the term angular frequency, it units is radian per second. For phase, it is also measured in radians or degrees, why is that? Why is the math the same when you use angles to describe oscillations?
21. ### Normal Modes and Normal Frequencies

Homework Statement I have to determine the frequencies of the normal modes of oscillation for the system I've uploaded. Homework Equations [/B] I determined the following differential equations for the coupled system: \ddot{x_A}+2(\omega_0^2+\tilde{\omega_0}^2)x_A-\omega_0^2x_B = 0...
22. ### Oscillation Equations

This probably has a very simple explanation, but I really need to know! What I really want to know is, is there any equation that relates the number of oscillations to other factors such as length, force applied, etc. to a simple plastic desk ruler (image attached)? (or) if there isn't one, how...
23. ### Oscillation speed question

Mentor Note -- thread moved from the technical forums, so no HH Tempate is shown...>> 1. (10 points) A pendulum of length l = 39 cm is suspended in a railway car. At what train speed would the pendulum be oscillating with largest amplitude ? The length of the rails is l = 25 m. I am just not...
24. ### I need advice on material to self-study physics (oscillations and waves)

I am currently in my second year of a bachelor of science with a major in physics. The class I am taking is notorious for being hard and the professor is very hard to understand (understanding the material, not what she's saying). The class is all about oscillations and waves. The textbook is...
25. ### How to find wavelength of wave?

Homework Statement A backyard pool is 14.5 m long. For fun Sally uses a board to create waves. Sally investigates the effect these waves have on Susan who is floating on another board near the middle of the pool. Sally notices that the waves travel with a speed 6.2 m/s. a) If Sally moves the...
26. ### Power of a sound source

Homework Statement A sound source is placed at the top of a tall (h = 189.6m) radio tower. The source has a frequency of 740 Hz and an amplitude of 19.4 nm at point A. The air surrounding the tower has a density of 1.29 kgm-3 and sound travels through it with a velocity of 343 ms-1. Point A is...
27. ### Oscillations due to restoring torque

Hi, My problem is with A.P. French vibrations and waves question 3-10, part (b). Question 3-10(a) A metal rod, 0.5 m long, has a rectangular cross section of area 2 mm2. With the rod vertical and a mass of 60kg hung from the bottom, there is an extension of 0.25 mm. What is the Young's...
28. ### Oscillation of a mass connected to a spring displaced

Homework Statement A mass m hangs on a spring of constant k. In the position of static equilibrium the length of the spring is l. If the mass is drawn sideways and then released,the ensuing motion will be a combination of (a) pendulum swings and (b) extension and compression of the spring...
29. ### The transmission profile in a fiber during tapering

I've been reading a article about pulling a fiber (or actually making it thinner until it becomes single mode). As the fiber's diameter decreases, the transmission profile of the light is showing oscillations. The frequancy of these oscillations increases as the fiber is getting pulled. But I...
30. ### Phase Difference with Initial Conditions for SHM

Homework Statement A mass-spring system with a natural frequency of 3.6 Hz is started in motion with an initial displacement from equilibrium of 6.1 cm and an initial velocity of 0.7 m/s. What is the value of ϕ? (Question aside: Finding the amplitude of the resulting function?) Homework...
31. ### Proportionality of frictional force

Homework Statement A mass-spring system consisting of a mass of 2.9 kg attached to a spring is subject to a frictional force which is both proportional and opposite to the velocity. The mass is displaced from rest and oscillates back and forth with an ever decreasing amplitude. It is found that...
32. ### Simple Harmonic Motion Question?

Homework Statement A 0.500Kg object is undergoing simple harmonic motion at the end of a horizontal spring with force constant k=300N/m. When the object is 0.012m from the equilibrium position, it is observed to have a speed of 0.300m/s. What is: a) The total energy of the object at any point...
33. ### Atomic clock: energy between two levels

Homework Statement With the atomic clock a second is defined as the time it takes for EM radiation to oscillate 9192631770 times, which equals the energy gap between two energy levels of a caesium-133 atom. Note: it's a translation and the term used with the oscillation is "oscillation periods"...
34. ### Find how far apart are the particles from each other

Homework Statement Two particles oscillate in simple harmonic motion with amplitude A, about the centre of a common straight line of length 2A. Each particle has a period of 3.3 s, and their phase constants differ by π/9 rad. (Assume the lagging particle starts at +A. Also assume that the...
35. ### Pendulum Oscillation Frequency?

Homework Statement Given a pendulum with fixed length, at what angle does the pendulum have to be released at in order to not follow the standard formula for frequency? Homework Equations P = 2pi*sqrt(l/g) The Attempt at a Solution I know that this equation holds for "small" angles (theta <...
36. ### Oscillation problem

Homework Statement mass "m" object is located near the origin of the coordinate system. External force was exerted on the object depending on the coordinate by the formula of Fx=-4*sin(3*pi*x). Find the short oscillation period, and the potential energy depending on the coordinate. Homework...
37. ### Central Hooke's Law Force

Homework Statement A particle of mass ##m## is placed on a smooth table and attached to a fixed point ##O## on the table by a spring with spring constant ##k## and natural length ##l##. (i) Show that the particle can execute circular motion about ##O## with angular velocity ##\omega## provided...