Period Definition and 997 Threads

From the original equation of ## \ddot{x}+x+\frac{3}{2}\beta x\lvert x\rvert=0 ##, I've got ## \ddot{x}\dot{x}+x\dot{x}+\frac{3}{2}\beta x\lvert x\rvert\dot{x}=0 \implies \frac{d}{dt}(\frac{1}{2}\dot{x}^2+\frac{1}{2}x^2+\frac{\beta}{2}x^2\lvert x\rvert)=0 \implies...

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Hello, I am currently doing research on the Foucault pendulum, specifically on its rotation period. I was wondering where I could find data concerning the observed rotation periods of various Foucault pendulums at different latitudes around the world (not calculated using the Formula T=24/sinλ)...

I'm doing a personal experiment where I take a conical spring (that is, a spring with two different diameters on either end), hang it from the ceiling, and measure the period of oscillation for different masses hanging below the spring. I do this for two different orientations of the spring; one...

I put 0, but that is incorrect. Why is 0 an incorrect answer? This is confusing, as if the pendulum is in free fall, wouldn't there be no SHM at all?

[Mentors' note: moved here from the technical forums after the thread was already fully developed, so no HW template] Hello all! I have a problem which I am beginning to suspect I am either unequipped to solve, or which does not have enough details! I can see, in my mind, the problem, but I...

By conservation of mechanical energy: $$ E(r_0)=-\frac{GMm}{r_0}+\frac{1}{2}\mu \left (\dot{r_0}^2+r_0^2 \omega_0^2 \right) $$ where R0 =Rmax. Because our body is located at the apoapsis the radial velocity is 0. Hence: $$ E(r_0)=-\frac{GMm}{r_0}+\frac{1}{2}\mu (r_0\omega_0)^2 $$ By the...

I want to ask about question (c). My idea is to compare the period and time constant. The period is 0.05 s and time constant is 0.005 s. Time constant is the time needed for capacitor to discharge until the charge stored in it becomes 37% of initial charge. But I don't know how to relate the...

Initially I went from: T = 2π√(2L/3g) T = 2π/√(3g) * √(2L) To finally this equation: T = 2π/√(3g) * √(L) Where 2L becomes L as the 2 is lost. I am not fully sure if this is correct or how to properly get rid of the 2 in 2L.We must follow the rule of y = mx+c whereby y = T, m = the constant...

Schutz finds that the orbital period for a circular orbit in Schwarzschild is $$ P = 2 \pi \sqrt {\frac { r^3} {M} }$$ He gets this from $$ \frac {dt} {d\phi} = \frac {dt / d\tau} {d\phi/d\tau} $$ Where previously he had ## \frac {d\phi}{d\tau} = \tilde L / r^2## and ## \frac {dt}{d\tau} =...

Hi ... I have answered this question and I think that F/mg equals 3. But I've asked it from someone and he told me that F/mg is 4. Can someone help me find out which one is correct ??? My answer :

For part (a) of this problem, The solution is, However why did say show the motion is periodic, but then the solutions don't show it, instead explain how it is periodic? Is there a way to prove that the motion is periodic other than the solution to part (b)? Many thanks!

I think the answer is just 1/10 (according to the formula for period), so the answer is 0.1. Is that correct? Thanks!

hi ! I'm having a lot of trouble simplifying my expression for one of my homework questions. I know someone asked about this homework problem already, but the answers didn't really help me figure out how to simplify it.. I really have no idea what steps to take, and I've even consulted all my...

The known expression of the wave function is where A is the amplitude, k the wave number and ω the angular velocity. The mathematical definition of arc length for a generical function in an interval [a,b] is where, in our sinusoidal case: For our purpose (calculation of the length in one...

Hi, I have been thinking about pendulums a bit and discovered that a HO(harmonic Oscillator) will take the same time to complete one period T no matter which amplitude A/length l it has, if stiffness k and mass m are the same. But moving on to a simple pendulum suddenly the time period for one...

In 1846 three astronomers and mathematicians discovered Neptune because Uranus wasn't quite moving as Newton's law of gravity explains. So they did calculations and point the telescope at a specific part of the sky. They discovered Neptune. What formulas did they use? How did they calculate this...

This question is related to Shor's algorithm and its use of modular exponentiation. In the table below, the period of the sequence in the third column is obviously equal to 4. That is, its value repeats every fourth row. What I am trying to find out is why it is that when the first value in...

When the platform moves with constant acceleration, the equation of Newton's 2nd law of motion is Forward force - W sin 30o = m.a Forward force = m (a + g sin 30o) ⇒ apparent gravity = a + g sin 30oFinal period of pendulum = ##\sqrt{\frac{g}{a+g \sin 30^{0}}} \times 2 = 2.38 s## Is this...

Based on the formulas, variable ##m , k, L,g## do not change so my answer is (a) but it is not correct. Why? Thanks

Hi, I am having to refresh my oscilloscope knowledge and am confused about one last function generator setting... Burst period. If I have 1 cycle at say 700 kHz it is 1.43us. If I set number of cycles to 10 then that is 10 * 1.43us = 14.3us time. This is my ON burst. So what is the burst...

hello, i have some diffuculties with this problem, there's the point where the spring is attached to the rod and according to the equation of time period of physical pendulum , h represent the distance from the COM and the pivot point. here the pivot point is at the COM. and i know that it can't...

I thought I would multiply b to the whole equation of T, but I have no idea how to formulate into the type of solution it wants

Find amplitude, period, PS, VS. graph 2 periods of $y=3\cos(\pi x-2)+5$ ok I think these are the plug ins we use $Y=A\cos\left[\omega\left(x-\dfrac{x \phi}{\omega} \right)\right]+B $ or $A\cos\left(\omega x-\phi\right)+B$ A=amplitude B=VS or veritical shift $T = \dfrac{2\pi}{\omega-\phi}$...

$$y=2 A \cos 2 \pi\left(\frac{\nu_{1}-\nu_{2}}{2}\right) t \sin 2 \pi\left(\frac{\nu_{1}+\nu_{2}}{2}\right) t$$ Can you explain me the significance of the above equation in the context of waves and oscillations? It's something to do with 'beats,'.

Find amplitude, period, PS, VS. then graph. ok I think these are the plug ins we use $Y_{cos}=A\cos\left[\omega\left(x-\dfrac{x \phi}{\omega} \right)\right]+B \implies A\cos\left(\omega x-\phi\right)+B \implies T=\dfrac{2\pi}{\omega} \implies PS=\dfrac{\phi}{\omega}$ ok I wanted to do...

I'm doing a lab report where I manually measure the time taken for a bifilar pendulum to do 10 oscillations. Is there a rule or a method that I should follow to calculate its uncertainty? Or is the uncertainty just an estimation of human reaction time and judgment? I also need to know the...

for (a) ##T=\frac {2\pi}{\omega}## $$\omega=\frac {2\pi}{T}$$ $$\frac{d \omega}{dt}=\frac {-2\pi}{T^2} \frac {dT}{dt} $$ $$\alpha=\frac {-2\pi}{(2.94*10^-15)^2} = 7.27*10^29 rad/s^2$$ for (b) I'm understand that it's infinity, because the period is increasing indefinitely, so it's slowing...

The owner of an ice cream shop kept records of the average number of sales per month for 2019. Create a sinusoidal equation to model this information of number of sales per month.I found the maximum, minimum for this, but how can I find the period of from this table. As I already know formula to...

$\tiny{\textbf{7.8.11 Campbell HS}}$ Find (A)mplitude, (P)eriod, PS, VS. graph 2 periods $y=3\cos(\pi x-2)+5$ by observation we have A=3 and VS=5 ok assume $\omega=\pi$ so if period is $T=\dfrac{2\pi}{\omega}$ then $T=\dfrac{2\pi}{\pi}=2$

This is not homework. I found this question when browsing and there is also solution but I do not understand it. This is part of the solution: My questions: 1) From equation (i): ΔT = m.a, I think ΔT refers to W - T (weight of block - tension of string). I got this from free body diagram and...

$\tiny\textbf{7.8.a09 Radford HS}$ Find amplitude, period, PS, VS. then graph. $y=\cos\left(x+\dfrac{\pi}{2}\right)$For the graphs of $y=A\sin(\omega x - \phi)$ or $y=A\cos(\omega x - \phi),\omega>0$ Amplitude $=|A|$ Period $T=\dfrac{2\pi}{\omega}=\dfrac{2\pi}{2}=\pi$ PS...

$\tiny{ACT.trig.01}$ What is the period of the function $f(x)=\csc{4x}$ $a. \pi \quad b, 2\pi \quad c. 4\pi \quad d. \dfrac{\pi}{4} \quad e. \dfrac{\pi}{2}$ well we should know the answer by observation but I had to graph it looks like $\dfrac{\pi}{2}$

The figure is shown; the measurements were taken on two consecutive observing nights. The Ordinate is the flux normalized to continuum and the abscissa is the wavelength scale. You can see the "bumps" indicated by the arrows referring to some Starspot as the spot moves on the profile; assuming a...

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...

My attempt at solving case B I've attached my attempt at case B above. What problem I'm facing is that after writing equation of angular SHM, I'm getting angular acceleration proportional to cube of angular displacement, which doesn't reduce to SHM. So how to find time period for this...

I've already found the potential and force that produce the given orbit. my results were: ##V=-\frac{al^2}{mr^3}## ##\vec{F}=-\frac{-3al^2}{mr^4}\hat{r}## Now, I've been trying to find the period using the equation ##t=\sqrt{\frac{m}{2}}\int_{r_0}^{r}\frac{dr'}{\sqrt{E-V_{eff}}}## Using...

Using this stimulation: https://phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_en.html It looks like frequency is decreasing as I increase tension but online it says frequency increases as tension does. Also, I am unsure about what happens to the Period

Hello :oldsmile: I have heard that various organisms in Carboniferous period had gigantic sizes because of relatively high Oxygen level in atmosphere. Today it is equal to 21 %, but at that time it was higher: https://www.nationalgeographic.com/science/article/carboniferous So, organisms...

I attempted this assignment, and scored a 5/10. The solutions are not given until a later date. I need to understand this material before I progress to the next section. The following are my attempts at the solution. The number of cycles in each pulse increases: The PD is determined by the...

I am currently studying Electrical Engineering and I have this question: An energy band is formed by the overlapping of atomic orbitals of atoms coming close to each other.I suspect that if the energy of the atomic orbital of the valence electrons of a chemical element is less than the energy of...

Hi, I know there's are 2 normal modes because the system has 2 mass. I did the Newton's law for both mass. ##m\ddot x_1 = -\frac{mgx_1}{l} -k(x_1 - x_2)## (1) ##m\ddot x_2 = -\frac{mgx_2}{l} +k(x_1 - x_2)## (2) In the pendulum mode ##x_1 = x_2## and in the breathing mode ##x_1 = -x_2## I get...

We can find that (1+e)/(1-e) = 8 => 1+e = 8 - 8e => 9e=7 => e=7/9. I'm not sure if I need this. We can also find the time period of Earth ## T=\frac{2 \pi r}{v} = 3.14* 10^7 s## I think I need more information from somewhere else. What am I missing?

This problem honestly got me in big confusion. I managed to find the angle ##\theta## at which the rod rests by equalling the components of weight and Lorentz's force... but from this point on I really don't know how to manage the harmonic oscillation part.

Let's say you have a leaking tab, and the probability of a droplet in any given second is 1%, regardless of whether there was a drop previously. How would you calculate the probability of n drops in a minute? No drops in a second is 0.99, so no drops over a minute is 0.99^60. Hence one or more...

The equation that governs the period of a pendulum’s swinging. T=2π√L/g Where T is the period, L is the length of the pendulum and g is a constant, equal to 9.8 m/s2. The symbol g is a measure of the strength of Earth’s gravity, and has a different value on other planets and moons. On our...

So my doubt is at the beginning of the problems hey are saying that the ball obeys stokes law and on the latter part of the question they are saying that no buoyant force is acting then how does the velocity of the ball change in the end? Also what is the use of specifying 'the ball never...

https://www.asi.edu.au/wp-content/uploads/2016/10/ASOEsolns2012.pdf Q11 D) Markers comments: Few students reached part (d) and very few of those who did realized that the amplitude does affect the time taken for each of Mordred’s bounces. i.e. the energy losses results in shorter periods...