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Why am I getting this derivation of time period of pendulum in an accelerated frame wrong?

starting with the free body diagram obtain the sum of the torques about point A $$\sum \tau=m\,L^2\ddot\theta+m\,g\,L\,\sin(\theta)- m\,a_a\,L\,\cos(\theta)=0$$ from here with $~\theta=\theta_0+\phi~$...
Eli's user avatar
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Why am I getting this derivation of time period of pendulum in an accelerated frame wrong?

Since the equilibrium angle $\theta_0=\arctan\frac{a_0}{g}\neq0$ has now changed, you cannot assume $\theta$ is small. Instead, you can define a shifted angle $\varphi:=\theta-\theta_0$, and use the ...
DanDan面's user avatar
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Potentials increasing faster than harmonic oscillator

I think this naturally follows from the way the energy gap changes. The way I think about this is this. Let's first stick only to HO potentials, but increase the frequency $(\omega)$, to vary the ...
freeElectron's user avatar
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Spherical quantum oscillator: Is energy smaller than the potential?

It is a general fact that for any state $\psi(\vec{r})$, we have $$\langle H \rangle > \langle V \rangle \geq \min V(\vec{r}).$$ The first inequality holds because the kinetic energy operator $\...
Michael Seifert's user avatar
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Can a harmonic oscillator never be Raman active?

Let me answer my own question based on the information I found in Chem. Rev. 1994, 94, 157-193 and PRL 119, 127402 (2017). The way I formulated the coupling of the HO to light, it would indeed not be ...
Rooky's user avatar
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How to visualize the angular frequency in SHM?

Consider looking at a rotating disk from above its axis of rotation. Lets say we have a point marked on the perimeter of the disk. The time it takes to complete a full rotation is the angular period ...
KDP's user avatar
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Direction of displacement

Displacement is relative. You cannot just be asked to provide a displacement. You must be asked to provide a displacement from somewhere. In a case like your SHM example, it would be reasonable for ...
Steeven's user avatar
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Direction of displacement

I think you need to define first what exactly does it mean to measure the position of a point (or a particle). You have some reference points (sometimes called the origin) and some unit directions (...
John Alexiou's user avatar
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Investigation Results of Damping of A Spring Showing Changing Phase Angle? Why?

Note: $$ \cos(\omega_dt + (\phi_0 + Bt)) = \cos(\omega't+\phi) $$ with $$ \omega' = \omega_d + B $$ so your damped frequency is wrong. So look at the above answer regarding error propagations, since ...
JEB's user avatar
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Investigation Results of Damping of A Spring Showing Changing Phase Angle? Why?

Welcome to the experimental world! To be fair, it's quite normal that oscillations do not perfectly coincides after some periods. You have a period of the oscillation $T \simeq 0.7 \, s$ and a shift (...
basics's user avatar
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Investigation Results of Damping of A Spring Showing Changing Phase Angle? Why?

I think this is just because there isn't going to be perfect agreement between the frequency in your fit function and the real-life frequency. Below are two sine functions that differ in frequency by ...
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Infrared regularizing the harmonic oscillator path integral

$a_0$ is the zero-mode of the Fourier-series of the position variable (1.45). It is therefore also the average (1.52) of the the position variable (up to a conventional normalization factor$^1$ $T$). ...
Qmechanic's user avatar
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Infrared regularizing the harmonic oscillator path integral

The product is the result of the integral for $n \neq 0$. The first term is $a_0$, the integral over the zero mode. That follows because $T a_0 = \Delta x$ via Eq. 1.52 and the following two sentences....
11zaq's user avatar
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Regarding to the asymptotic solution of quantum harmonic oscillator

You need to be careful on defining the asymptotics. From the equation: $$ u''+\left(\epsilon-x^2-\frac{l(l+1)}{x^2}\right)u = 0 $$ you want to know the behaviour of $u$ at infinity. The issue is that ...
LPZ's user avatar
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1 vote
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Two Simple Harmonic Motion (S.H.M.) in Perpendicular Direction

It is perhaps easiest to look at a non-generalised example? A position in the x-y plane, $(\sin(2\pi f t)\,,\,\sin(2\pi f t\pm \phi)$ which depends on time $t$ and where $f$ is the frequency and $\phi$...
Farcher's user avatar
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2 votes

Two Simple Harmonic Motion (S.H.M.) in Perpendicular Direction

Consider an example of a circular trajectory: $$\mathbf{r}(t)=\cos(t)\hat{\mathbf{x}}+\sin(t)\hat{\mathbf{y}}$$ We can rewrite this purely in terms of cosines, by remembering that $\sin(t)=\cos(t-\pi/...
Riley Scott Jacob's user avatar

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