Pendulum Definition and 1000 Threads

I want to create a method to calculate acceleration of blobs in any degree pendulum (double, triple and more). I have this equation but I am not sure if it is correct, or how to extract acceleration from it. [Mentor Note -- this is a new thread start to correct errors in the previous 2 thread...

(a) No, a person seated inside the train compartment will not be able to tell whether the train is accelerating on a horizontal track or moving uniformly up an inclined track by observing the plumb line. (b) I am assuming that both observers are not allowed to look "out" of the boundaries of...

Consider a conical pendulum like that shown in the figure. A ball of mass, m, attached to a string of length, L, is rotating in a circle of radius, r, with angular velocity, ω. The faster we spin the ball (i.e., the greater the ω), the greater the angle, θ, will be, and thus, the smaller the...

I refer to the website below (for more information): http://www1.lasalle.edu/~blum/p106wks/pl106_Pendulum.htm#:~:text=The forces acting on the,the tension of the string.&text=The net radial force leads,is v2/r.) P.S. I'll insert my specific questions in the following paragraphs in this format...

This is the figure given. My Attempt ##T=2\pi \sqrt\frac {I}{0.5gd}## ##\frac {m_r} {l} ## ##dm= \frac {m} {l}dx## ##dI = dm_r x^2## ##dI=(\frac {m_r} {l}dx)x^2## ##I= \int_l^0 (\frac {m_r} {l}dx)x^2 \, dx ## ##I_c.m=\frac {m_r l^2}{3}## ##I_,, = \frac {m_r l^2}{3}+m_p x^2## Given...

By Lagrange's formalism, the motion equations for double pendulum are: Using Newton's formalism I can't obtain the second equation. Anyone can help?

I must find the Lagrangian for an undamped pendulum using the diagram showed below, I've no idea what to do with the second angle φ2 because is measured from the line that joins the two pivot points. The ecuations I must obtain are as follows I get so many different things but I can't reach...

Hello! I need some help with this problem. I've solved most of it, but I need some help with the Hamiltonian. I will run through the problem as I've solved it, but it's the Hamiltonian at the end that gives me trouble. To find the Lagrangian, start by finding the x- and y-positions of the...

Hello! So we are given this very interesting physics question, that we should only discuss and not do any calculations. So for a) I've though this if the clock is running too fast,the way to adjust this would be to lengthen the pendelum length,my logic behind this the longer the pendelum the...

Hi guys can someone look at my work for uncertainty and let me know if it makes sense.

I've just studied simple pendulum: The simple pendulum (for small oscillations) differential equation is first image. I've no problem to arrive this result and formula. My problem is to get to the second formula by passing through another formula (Image 3) that my book mentions. I can't...

Pendulum plane, which suspension executes a horizontal harmonic motion $$x = acos(\gamma t)$$ Position P, orientation x to right and y points below, phi is the pendulum's angle wrt y. $$P = (acos(\gamma t) + lsin(\phi(t)), lcos(\phi(t)) )$$ So executing all that is necessary, i found it...

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...

Hello! I have some problem getting the correct answer for (b). My FBD: For part (a) my lagrangian is $$L=T-V\iff L=\frac{1}{2}m(b\dot{\theta})^2+mg(b-b\cos\theta)-\frac{1}{2}k\boldsymbol{x}^2,\ where\ \boldsymbol{x}=\sqrt{(1.25b-b)^2+(b\sin\theta)^2}-(1.25b-0.25b)$$ Hence my equation of...

a) This looks somewhat like a pendulum problem (length ##\ell/2##). I reasoned there will be a clockwise rotation, and that the acceleration is due to the force of...

Here is an image of the problem: The problem consist in finding the moviment equation for the pendulum using Lagrangian and Hamiltonian equations. I managed to get the equations , which are shown insed the blue box: Using the hamilton equations, i finally got that the equilibrium angle...

Here is an image of the problem: The problem consist in finding the moviment equation for the pendulum using Lagrangian and Hamiltonian equations. I managed to get the equations , which are shown insed the blue box: Using the hamilton equations, i finally got that the equilibrium angle...

Question 1: A pendulum 2.2m long has a mass of 8.5kg suspended from it. The pendulum is initially in a vertical position and is moved to new position 35 degrees from the vertical. (a) How much work is required to move the pendulum to its new position? (b) If the pendulum swings from this...

I need help to understand this problem taken from Mechanical Vibrations by S. Rao I know that the equations of motion could be obtained in various ways, for example using the Lagrangian, but, at the moment, I am interested in understanding the method he used. In particular, if I'm not...

That's a good question, i am not sure how the water in liquid state will influence in the motion, but i imagine that can not exert any torque, i would say in the first case: Hollow sphere inertia moment: 2mr²/3 + ml² (2mr²/3 + ml²)θ'' = -mglθ (1) In the second case, otherwise, we will have...

The problem is how to construct the right diagram of forces actually Unfortunately, the Fo*cos acting on the ball will not carry the g/l of the solution -mg*sin(´p) + (-bv) + (Fo*cos(wt)*cos(p)) = mx'' Fo*cos(wt) = mx'' + mg*x/l + bv

My answer to part A is correct but for Part B I got an incorrect answer of 0.204J. My working out is sent as an attachment. Part A: Part B: Part C:

Let me ask a very primitive question. To and fro motion of pendulum under gravity tells us potential energy + kinetic energy = const. At the top points potential energy: max kinetic energy :0 At the bottom point potential energy: 0 kinetic energy :max EM wave is usually illustrated as...

Summary:: Calculate the quantum number of a pendulum I want to calculate the quantum number of pendulum. L = 1m, m = 1 kg., A= 3cm. I get a period of 2.01 sec. and f = 1/T = .498 sec. E =nhf gives me 2.67x10^31. The correct answer is 1.33x10^31, Where am I going wrong? [Thread moved from...

Given the total angles in the x direction, I set up this: (mg/cos(x))*sin(x)-Fe=0 then isolated for x: mgtan(x)=(kq^2)/(2*sin^2x) sin^2(x)*tan(x)=(kq^2)/(2mg) From here I am stuck. How do I go forward when x is contained in two different trig functions on the left?

I did the first step pretty well, and the answers match, but i don't understand why in the second case the period changes.

Hello, I've got to rationally analice the form of the solutions for the equations of motion of a simple pendulum with a varying mass hanging from its thread of length ##l## (being this length constant). I approached this with lagrangian mechanics, asumming the positive ##y## direction is...

Hello everybody, new here. Sorry in advance if I didn't follow a specific guideline to ask this. Anyways, I've got as a homework assignment two cannonical transformations (q,p)-->(Q,P). I have to obtain the hamiltonian of a harmonic oscillator, and then the new coordinates and the hamiltonian...

If the bottom disk is free to spin, will it necessarily spin? all the forces in this disk don't produce a torque. I don't know why we disregard it's inertia moment when it is free to spin (It's intuitively set, but I can't see it mathematically) :\

"A pendulum is made of two disks each of mass M and radius R separated by a massless rod. One of the disks is pivoted through its center by a small pin. The disks hang in the same plane and their centers are a distance I apart. Find the period for small oscillation" I don't understand why we...

Suppose we displace the pendulum bob ##A## an angle ##\theta_0## initially, and let go. This is equivalent to giving it an initial horizontal displacement of ##X## and an initial vertical displacement of ##Y##. Let ##Y## initially be a negative number, and ##X## initially be positive. I observe...

Hi All, Anyone willing to help out in explaining what eigenfreuqncy for this oscilatory system, would be? Also if anybody knows the equation to calulate this stuff please, if you're willing to share I'd be greatful! Thanks, regards.

The diagram for the problem is shown alongside. In the vertical (##\hat z##) direction we have ##T \cos \theta = mg##. In the plane of the pendulum, if we take the pendulum bob at the left extreme end as shown in the diagram, we have ##T \sin \theta = \frac{mv^2}{r}## (the ##\hat x## axis of...

I am using the Stanford “Dynamics: Inverted pendulum on a cart” document, https://web.stanford.edu/class/me161/documents/InvertedPendulumOnCartSolution.pdf, as the basis for the Arduino c code. I need help with the term Fc (Feedback force on the cart A) because the motor I’m using is a stepper...

I'm confused about how to find the final value of g and its uncertainty. I've done a bit of research and I have encountered conflicting information, some say you have to weight the measurements, some say you have to find the standard deviation then divide by two, etc. I have the following...

The question :- My attempt :- The confusion that I am having is that to get the required form of the equation of motion, I had to approximate ##\theta## to be small to get ##x=l\theta## so that I could get the acceleration and the velocity. But, I had to leave the ##sin(\theta)## in the...

In this experiment, I still can't figure out why the graph between time period and distance from point of oscillation is like that. Why does it first decrease and increase so steeply? I got the second part because it goes near the centre of gravity and time period becomes almost infinite there...

I know that the potential of a simple pendulum is given by the above formula and that we can expand ##cos\theta## to get ##V=mgl\left(\frac{\theta^2}{2}-\frac{\theta^4}{24}+...\right )## I am guessing that the answer is ##\theta^4##, but I am not sure what "order" means here.

The question is My attempt is given below I am not sure what to do now. I don't understand how I can make the coefficient of ##cos\theta## negative.

So I have been given a question here which asks me to work out the maximum kinetic energy of the pendulum It has given info such as time period and amplitude, which I had then made use of these formulas Does a kinetic energy of approx 50.98 micro joules seem right here? Any help would be...

Consider the following setup: In this, let us set the pendulum 1 into motion. The energy gets transferred through the connecting rod and the other pendulum starts oscillating due to the driving force provided by the oscillating pendulum 1. Isn't it? So the neighbouring pendulum starts...

So in this instance height is longer than the 3m string which is impossible. Do we just say that when ever H>L, H=L?

I have measurements of period time and distances that's all: T (sec) D (m) 0.9 0.008 0.91 0.009 0.97 0.01 0.98 0.011 1.06 0.012 I thought about adding the magnetic force like: T=2π*√l/(g+x) but have no clue how to integrate the distance there, I don't know even how to start...

I am not sure which other forces I should consider besides those 3. I cannot consider tensions due to the massless rod on the masses since those will not add up to zero.

I'm interested in calculating effective gravity for a point-mass in a spinning gyro or swinging pendulum bob on a rotating planet undergoing any translational velocities and/or accelerations. I want to investigate the theoretical effects of high-energy mechanical oscillation on orbital...

I tried taking log and then diffrentiate the standard equation for time period of a pendulum but i am not getting the correct answer

The equation of motion of a simple pendulum is: $$\ddot \theta + \frac{g}{l} \theta = 0$$ Our Physics professor told us: 'If you want to become a good Physicist you have to be able to analytically check your answers to see whether they make sense'. In class he took the limits of constant...

Where: 1) ##A## is the translational acceleration, ##\Omega## the angular velocity and ##\dot \Omega## the angular acceleration (all relative to the inertial frame attached to the ground ##F##). 2) ##r'##, ##v'## and ##a'## are the position, velocity and acceleration vectors, all relative to...

I got this picture from a superconducting parametric amplifier text I was reading. (The picture is a mechanical analog of a non-degenerate parametric amplifier.) If the balls(red and blue) were oscillating at their own natural frequencies, and an external force is driven(purple), how would the...