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Questions tagged [oscillators]

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Time Period of Oscillations ( A mechanical problem) [on hold]

So , basically I came across the following question : A massless rod (lying on a frictionless horizontal plane) is hinged at a point O. A string carrying a mass m at one end is attached to point A ...
6
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1answer
93 views

Oscillation of Chocolate bar on soda

Why does a piece of chocolate bar oscillate in soda (i.e. floats then after a while sinks and vice versa)? What parameters does the period of oscillation rely on? Is there a specific formula that ...
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3answers
44 views

Rotational Kinetic Energy of a Pendulum

By the parallel axis theorem, a pendulum that rotates around a point $P$ and a distance $l$ from it's center, has kinetic energy $E_{kin}= \frac{\omega^2}{2}(\frac{2mR^2}{5}+ml^2)$. Where R is the ...
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0answers
34 views

Why a musical instrument's string oscillates with many frequencies? [duplicate]

I am trying to understand why when we play a note on a stringed instrument, not only it oscillates with it's fundamental frequency but also the multiples of that. For instance if you play a D on the ...
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1answer
22 views

Effect of elasticity of string on simple pendulum

In a simple pendulum system, how does the extensibility/elasticity of the string affect the time period of oscillation? Would it lead to a random or systematic error? Would the elasticity of the ...
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6answers
1k views

Springs with some finite mass

Let us consider a spring which is having some finite mass. By the help of some external agent the spring has been extended by some distance $x$. Will the restoring force produced in the spring still ...
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2answers
47 views

When you increase the tension on a string, how is the standing wave affected?

I know that wave velocity is the product of wavelength and frequency, and that velocity is proportional to string tension. Does this mean that if you increase the tension on a string, the wavelength, ...
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2answers
39 views

Does damping force depend on frame of reference?

I learn that damping force with regard to forced damped oscillations is given by F = -bv where is the velocity of the object measured from ground frame. Suppose we are in a frame which is moving with ...
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1answer
59 views

Time period of an oscillatory motion [closed]

The question: A particle of mass $m$ is executing oscillation on the $x$-axis. Its potential energy is $U(x)= K|x|^3$, where $K$ is a positive constant. If the amplitude of oscillations is $a$, ...
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2answers
152 views

Why the time period of pendulum with infinite length is $84.6$ minutes? [closed]

In a book I was reading about SHM it stated: If the length of a simple pendulum is increased to such an extent that $\ell\to\infty$, then its time period is given by, $$T=2\pi\sqrt\frac{R}{g}\...
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1answer
42 views

Pendulum in a Boat [closed]

Suppose a pendulum is kept in a boat and it is oscillating. Now if the boat is made to oscillate in the same direction or opposite to that of the pendulum, how will these affect the amplitude of the ...
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5answers
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How can I prove that a state of equilibrium is unstable?

In the particular problem I encountered, an electric field was zero at the origin and we were meant to prove that a particle at the origin was in an unstable state of equilibrium. Is it enough to ...
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3answers
77 views

Potential energy of an oscillating pendulum

The following question always confuses me. for an oscillating pendulum why the potential energy is given by: $$V = mgL(1-\cos\theta)$$ Why not $$V = mgL\cos\theta$$ Is this a convention or there ...
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0answers
47 views

How long does it take for a wave pulse on a string to get reflected from rigid boundary?

This question arises from analysis of standing waves.The incident wave has the equation $$y=Asin(kx-\omega t)$$The reflected wave has the equation$$y=Asin(kx+\omega t +\pi)$$When determining the ...
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0answers
28 views

Stationary waves in a string

The narrator says that 'the ends will be taken as nodes' while to generate the wave, the simulation is oscillating the left end. I was taught that a node has zero amplitude; here that is not the case. ...
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3answers
48 views

Inserting an arbitrary phase in the equation for driven damped oscillations

In Classical Mechanics by Taylor, we find the solution to the differential equation of a damped oscillator with a sinusoidal driving force: $$\ddot{x} + 2\beta\dot{x} + \omega_0^2x = f_0\cos\left(\...
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1answer
48 views

Is energy conserved in a Van der Pol oscillator?

The Van der Pol Oscillator is governed by a 2nd order ODE with nonlinear damping. The 'position' of the oscillator is the solution to $$x''(t) = \mu (1 - x^2(t)) x'(t) - x(t)$$ Here $\mu$ controls ...
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1answer
28 views

What does the viscous damping coefficient depend on?

I’m doing a theoretical calculation involving the damping on an oscillating string, and I found the following relationship, where a certain damping factor $b$ is proportional to $\frac{c}{d^2}$ where $...
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0answers
42 views

Prove from first principles that a guitar string will vibrate at a constant frequency

From experience I am aware that a taught string will generally vibrate with a constant frequency. I wanted to prove this by considering the relation of distance from the resting position, and its ...
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1answer
70 views

What is complex frequency? [closed]

I am learning EE, and about complex frequencies, but what is its physical meaning? What is it used for? Why is it? And only happen in the laplace transform?
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1answer
77 views

Difference between simple harmonic motion and angular SHM

I am not able to decipher when it is simple harmonic motion and when it is angular harmonic motion. Can we use both of them interchangeably? Can I know all the variable analogous for angular SHM (by ...
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1answer
24 views

Oscillations - Mass Change on Simple Pendulum

The problem that I am thinking of is phrased as follows: A person on a swing is holding a sandbag and is moving with some initial velocity $v_0$ at the bottom of the swing of length $l$. The ...
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4answers
75 views

Solutions to Newton's laws with unbounded kinetic energy for inverted harmonic oscillator potential

In a one dimensional setting, Hooke's Law, together with Newton's 2nd law, results in a differential equation of the form (setting the constants $m$ and $k$ equal to 1 for notational simplicity) $x''(...
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1answer
37 views

Could the flex in a skyscraper due to wind be used to produce power?

While browsing 'Hot Questions' on Stack Exchange I came across this question: Can we use the stored gravitational potential energy of a building to produce power? It got me thinking about the use of ...
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2answers
27 views

Materials used for damping

What type of material should be used for damping? Like my course says ductile materials but then if the damper is deformed it wont be able to be used again, so how does that work? Like why not stiff ...
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2answers
44 views

Energy transfer through damping

When a damper is attached to a bridge, its tuned to the bridges natural frequency. I dont get how will that allow for maximum transfer of energy? And also how will heavily damped systems prevent ...
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1answer
154 views

Applying Kramers-Kronig relation to a simple damped oscillator

I just discovered the Kramers-Kronig relation and am trying to apply it to a simple damped oscillator of the form subjected to an impulse at $t=0$, which is a causal system: $$m\ddot x + c\dot x + k ...
2
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1answer
77 views

How to obtain the quantization of a simple pendulum using Bohr-Wilson-Sommerfeld rule? [closed]

How to obtain the quantization of a simple pendulum using Bohr-Wilson-Sommerfeld rule?
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1answer
25 views

Small amplitudes and Stokes drag law

Why is it that on a damped harmonic oscillator or a pendulum in a fluid, the Stokes drag law in the fluid only applied to small amplitude oscillation compared to large amplitudes oscillations? Dose ...
0
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1answer
62 views

To consider or not to consider potential energy of a mass attached to a spring in oscillation? [closed]

For the above system I have the following expressions for kinetic and potential energy: $$ V = \frac{1}{2}\,k\,x^{2}+m\,g\,l\,(1-cos\,\theta)-m\,g\,x\\ T = \frac{1}{2}\,m\,\dot{x}^{2}+\frac{1}{2}\,m\,...
0
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1answer
20 views

Damped oscilliations on a ball rolling in a U-shape

How do you calculate the rate of loss of energy on a ball moving in a U-shape (half sphere)? Can I simply look at the height of the ball at its peaks and measure the difference between the potential ...
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2answers
42 views

Restoring forces and oscillating systems

My book states, 'Restoring forces give the system it's potential energy.' And it also states, 'Inertia due to mass in mechanical system gives the system it's kinetic energy.' I don't get what is all ...
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2answers
81 views

Why $y=A\sin(kx-\omega t)$ is used in deriving standing wave equation? [closed]

In my text book equation of travelling wave is given as $y=A\sin(\omega t-kx)$ and they deduced standing wave equation using the same wave equation and arrived at $Y=2A\cos(kx)\sin(\omega t)$ but ...
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1answer
90 views

Why is frequency equal to the inverse of period?

I am really struggling with this concept, please help. I know that the period is simply the time for 1 for one complete cycle, but how come the frequency is 1 over this? It is confusing to me
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1answer
45 views

Finding the Amplitude of a Spring Oscillation given initial Position and Velocity

I'm trying to create a physics simulation, and I need to be able to determine the amplitude of the oscillation of a mass-and-spring system given any position that the mass might be in and the velocity ...
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1answer
37 views

Oscillations and Spring balances problem

Problem Statement: A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released oscillates with a ...
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2answers
33 views

Damped drive oscillating systems

I am currently looking at the theory of find the viscosity of and object through damped harmonic motion, and tho it can be done there is obviously a limitation with regrades to the medium. If the ...
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1answer
184 views

How to derive a formula for the period of a simple pendulum? [duplicate]

The following formula is given in our lab manual: $$ T = 2 \pi \sqrt{\frac{L}{g}} \left( 1 + \frac{1}{4}\sin^2 \frac{\theta}{2} + \frac{9}{64}\sin^4 \frac{\theta}{2}+\cdots \right) $$ for the period ...
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1answer
33 views

Understanding a reference (Cummins on 2d order ODE)

In the first page of The Impulse Response Function and Ship Motions (Cummins, 1962), it is written that: We can now write an equation, which has the appearance of a differential equation, relating ...
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1answer
37 views

Swing - time taken [duplicate]

I was thinking about how I would go about calculating the time taken for a swing to swing from one side to the other, assuming that there only exists a gravitational force and discarding all other ...
0
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2answers
66 views

How is the simple damper equation derived?

I know the spring is modeled as $F_{\text{elastic}} = k\cdot x$ when the displacements are small since this is empirically based, but what happens with $F_{\text{damping}}=c\cdot\dot{x}$? It is the ...
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1answer
54 views

Single-mode hamiltonian

I´m a bit stuck with an exercise I have to do for a class of mine. We have been given a Hamiltonian $$\hat{H}=\hbar\omega\hat{a}^{\dagger}\hat{a}+\hbar\theta\left(\hat{a}^2+\hat{a}^{\dagger 2}\right)...
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2answers
44 views

How does a sound box amplifier work?

I read in a few places that in a guitar for example, the vibrations are passed through the connectors to the wood and the wood with its bigger surface is more efficient as a coupler to the air, ...
3
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1answer
78 views

How fast can we walk? [closed]

It has been a common observation that as and when we accelerate ourselves, there comes a point after which we cannot stay on the ground completely. I wanted to know whether we can find such a maximum ...
0
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3answers
75 views

Is natural frequency of an LC circuit equal to angular frequency ? Why don't the units match?

When I was reading the L-C circuit in my textbook I came across the derivation of equations of instantaneous charge and current. Which is no problem, but when I got to the derivation to current . ...
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0answers
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Spring with oscillating support (Goldstein chapter 11, problem 2)

The problem: 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 ...
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1answer
58 views

Green's Function Method for a Spring and mass system [closed]

I think I've done part a) correctly and I have a general solution. However, I now have two unknown constants in my general solution and, as far as I can see, only one condition ($x(0)=-1$) with which ...
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3answers
55 views

$Q$-factor for damped oscillator (not driven)?

How would this be defined? Some of the Q-factor definitions I have encountered include: $$Q=2\pi\frac{Energy \space stored}{Mean \space power \space per \space cycle}\\Q=2\pi\frac{Energy \space ...
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1answer
90 views

Small Angle Approximation for Simple Pendulum

I am working on a simple pendulum problem. The $y$ direction is vertical and the $x$ direction is horizontal. Displacement in the $x$ direction is taken to be much less than the length of the string, ...
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1answer
92 views

Why is a parallel RLC circuit usually driven by a current source?

Almost always when I see an example of a parallel RLC/LC circuit diagram online, the circuit is driven by a current source instead of a voltage source. On the other hand, the series RLC is always ...