Pendulum Definition and 1000 Threads

I know that mass does not affect the acceleration in a simple pendulum undergoing SHM, but how does the mass on the spring that makes up the elastic pendulum affect its acceleration? Certainly, there must be a change due to the displacement from equilibrium caused by each differing mass? I am...

[Mentor Note: Two threads on the same project have been merged into one] I need serious help with this. I'm totally stuck as to why my results are mediocre. It would mean a ton if someone could at least point me in the right direction. Below is my attempt: import matplotlib.pyplot as plt...

First, we construct a simple pendulum, the length of the rope remains unchanged and the object being swung is doing circular motion. If it is released from point D and reaches point F, we set: The length of the rope (i.e the pendulum length) is L, ∠FCB=90°, ∠DCF=β, ∠ECF=α, the mass of the...

I want to calculate the equation of motion of a planar pendulum of length l with a mass m at its end and a pivot point that moves uniformly along a vertical circular path (radius a) with a constant frequency ω. The Lagrangian and the equation of motion for a planar pendulum with a moving pivot...

Hi everyone, I am going through the book called "Numerical Methods for Engineers" and I am trying to solve for the angle of displacement of a pendulum. I am using MATLAB to do this. However, I am getting some strange results. In the book the differential equation is: Because this is a...

I imagine the setup to be like this: the pendulum is moving horizontally, then it will experience electric force upwards so there is additional upwards acceleration, in addition to the acceleration from restoring force. Since the resultant of the two accelerations is not directed horizontally...

Here are some diagrams: The mass of the rod is M, and the external cylinder is m. This is what I came up with:

Last time I posted to the forums I was told to use some type of text thing to make equations easier to read for clarity, but I can't figure it out, so sorry if this is hard to read. I know that d = 10-r After making a free-body diagram, I thought the circular force had to equal Tension +...

In the formula above I have that the mechanical momentum of the horizontal force with respect to ##C## is always ##0## because the point of application coincides with the pole. Also, the mechanical momentum of the costraint reactions is ##0## because the costraint is smooth so the reaction is...

Let ##m_{r}=1## kg be the mass of the rod and ##m_{s}=0.5## kg be the mass of the sphere. ## \tau = -rFsin\theta ## ## = -r([m_{r}+m_{s}]g)sin\theta ## ## =-1.3(1.5)(9.8)sin30 ## ## \tau = -9.6 ## My book's answer key disagrees and my initial thoughts are that maybe the mass in my...

Let the origin be where the pendulum string is attached to the ceiling. $$\sin{\theta(t)}=\frac{x(t)}{L}\tag{1}$$ $$\cos{\theta(t)}=\frac{y(t)}{L}\tag{2}$$ $$\theta(t)=\sin^{-1}{\frac{x(t)}{L}}\tag{3}$$ $$\dot{\theta}(t)=\frac{\dot{x}(t)}{\sqrt{L^2-x^2(t)}}\tag{4}$$...

Consider a simple pendulum as depicted below Consider the integral $$\int \vec{F_g}\cdot d\vec{r}$$ My question is if we can equate this to the negative of a change in a potential energy function, ie ##-\Delta U##? Since ##F_g## is conservative, by the 2nd fundamental theorem of calculus...

For this part (b) of this problem, From (a), we know that ##\mathcal{L}\left(\phi_{1}, \phi_{2}, \dot{\phi}_{1}, \dot{\phi}_{2}\right)=\frac{1}{2} m \ell^{2}\left[2 \dot{\phi}_{1}^{2}+\dot{\phi}_{2}^{2}+2 \cos \left(\phi_{1}-\phi_{2}\right) \dot{\phi}_{1} \dot{\phi}_{2}\right]+m g \ell\left(2...

I'm engaged in a research project focused on pendulums. I'm trying to model a rigid pendulum's motion with a second order differential equation (where time is the independent variable) describing the relationship between θ (theta) , ω (omega) and α (alpha) where: - θ is the angle of the...

The problem and solution are, However, I don't understand why the answer is correct. I think that time should be dilated since ##\Delta t = γ \Delta t_0 = 2γ## where ##γ \geq 1## for ##v \geq 0##. Does anybody please know what I'm doing wrong here? Thanks!

Sorry for the overly general title but my problem is regarding a specific problem: find the net force on the bob of a pendulum as a function of ##\theta##, the angle it makes with the vertical (assuming the observer is stationary with respect to point from which the string is hung and the...

TL;DR Summary: An impulse is given to the pendulum so that it moves in 3 dimensions. What equations apply throughout its motion? A particle of mass ##m## is suspended from a string of length ##\ell##. The string is then deflected at an angle ## \theta ##, where the particle and string are in...

For this problem, My working for finding the coordinates of the mass is, ##x = x_p + x_m = R\cos(\omega t) + l\sin(\phi)## ##y = -y_p - y_m = -R\sin(\omega t) -l\cos\phi## However, I am told that correct coordinates of the mass is ##x = x_p + x_m = R\cos(\omega t) + l\sin(\phi)## ##y = y_p -...

For this problem, I am confused my what they mean by ##\phi##. I have looked at the figure, but it is confusing. Makes it look like the x-axis and y-axis are not perpendicular, even thought I'm assuming they are since this is a right handed coordinate system. Does someone please know what...

For this problem, The correct coordinates are, However, I am confused how they got them. So here is my initial diagram. I assume that the point on the vertical circle is rotating counterclockwise, that is, it is rotating from the x-axis to the y-axis. Thus ## \omega t > 0## for the point...

For this problem, I correctly got the same coordinates for the pendulum mass using another coordinate system. The coordinate system I used was the other coordinate system rotated counterclockwise by 90 degrees. Why is the pendulum mass coordinates invariant in my cartesian coordinate system...

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Hello. This is the figure of the problem: First, we should determine the Lagrangian of the system. I have already completed this part without any issues. To respect everyone’s time, I won’t go into the details of how I accomplished it. $$L=\dfrac {M+m}{2}\dot x^2+ml\dot x \dot \theta \cos...

Pretty much what the title says. Everything that I can find online addresses the pendulum problem with the assumption that the rope is under tension to start. What if the rope is slack to start? Will there be an increase in force applied to the pivot point, say if a mass is dropped off a...

I'm the technical director for a theatre group and am looking at the best way to get an actor to use a rope to swing on stage. As we rent the theatre we use I need to run everything by their staff, who doesn't have a solid grasp of mechanics and physics. I proposed that we lower a pipe from...

I tried using the formulas x=xi+vit and y=yi+voyt-1/2g(t^2) I assumed voy would be 0 and I almost arrive to the answer but idk how to get rid of the negative

I move the system by a small angle θ . I am not sure if my calculations of kinetic and potential energy are correct.

Hi all, This is a question that has been bothering me and applies to kinetic sculptures. Let's say you have a wheel. The wheel is situated in the vertical plane (like a clock hanging on the wall). For the sake of easy math, let's say the wheel has a radius of 1m, and has the entirety of it's...

idk

I have a problem with the method that they solved. This is what I mean ##\delta t= \frac{\pi L\alpha \delta T}{\sqrt{gL}}##. You can derive this equation by using errors and approximations here delta t is a tiny(not infinitesimal) change in time period, delta T is a tiny change in temperature...

I put the answer as (IV) but that happens to be wrong (or maybe it was only one of the multiple correct answers). Here is my reasoning: I. the force is dependent on mass, but isn't always constant. II. It's not always in the same direction, it points towards the rest point. Consider a point at...

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?

Started by analyzing the change in energy from the initial position to the final position which gives us mgh=1/2mv^2 Since we are trying to find speed, we rearrange the equation to solve for v, which gives us √2gL. My question is, do we need to take a component of L for √2gL because it is at...

While not exactly correct, we will continue to use Newtonian gravitational force and tension force in the lab frame. We will not concern ourselves with GR, besides the approximation is reasonable for low velocity and small mass. In the lab frame, the forces acting on the pendulum is weight and...

Consider a pendulum swinging at the North Pole in an inertial frame of reference xyz with the x and y axes in the plane tangent to the pole and the suspension placed at elevation z = l. There is no induction \mathbf{B} and in the chosen system the plane of oscillation xz of the pendulum is...

Hi, I'm working on a simple benchmark problem for FEA. It's a pendulum initially positioned at an angle of ##45^{\circ}## and then subjected to gravity. I'm interested in the maximum velocity (when the pendulum is in the vertical position). So far, I've been using this formula: $$v=\omega \cdot...

All double pendulum have same inital position, start from same height at same time, this softwear must have some equations from which calculate their path, so if both use same eqution and same inital position, why they have different paths(this is mathematicaly impossible)? One question about...

Hey guys, Can someone help me understand how to understand this problem intuitively please? How I understand is that I need to look the acceleration relative to the lift as if it were f.e. on another planet with a different acceleration. this gives me a = g - 5. But then again if I didn't look...

Suppose there is a very large mountain adjacent to a pendulum such that there is a horizontal component gravitational force of ##10^{-5}g## acting on the otherwise ideal pendulum. How would one use a perturbation to add that effect to first order? My initial thought would be to figure an angle...

Consider the standard pendulum with a weightless rod of length b and a mass point m and mg is applied. In the hinge there is a torque of viscous friction which is proportional ##\omega^2##. Now release the pendulum from the horizontal position. What biggest height does the point m attain after...

TL;DR Summary: I am doing an experiment for my Physics IA and don't know the theory behind it I am working on a Physics experiment for my school where I vary the distance between a simple pendulum and an aluminium block, and get the damping coefficient for each distance. Below are the images...

Recently, in this forum, highly respected members referred to clocks like pendulum and hourglass as if they are relevant for relativity. Are they really? Besides the lack of accuracy, they depend on acceleration/gravity, so they would not work at all in inertial frames and they could not...

I was able to solve first part I.e. time period of the system when bearing has friction I am unable to figure it out why disk will not rotate when it is mounted to frictionless bearing ? I know that due to absence of friction disk cannot rotate but then Mg is also there which can rotate the...

I don't understand the question. how am I supposed to find the magnitudes and directions of the velocity from the figure?

A recurring question is: while the motion of a polar Foucault pendulum is fairly straightforward, the case of a non-polar Foucault pendulum is quite difficult to visualize. In 2020, on physics stackexchange someone submitted that question and I contributed an answer. In a comment to another...

Hi All, My goal is to relearn some control theory and implement a working inverted pendulum on a cart with an industrial linear motor. See video: Working through an example of an inverted pendulum on a cart posted here...

I need to write an equation for Newton's second law for the above system, where k1=k2 (both springs are the same). The red line represents a bar with m=2kg, l=2m. I know that I*α = M1 + M2 + M3 If we displace the bar by x, we get the angle of displacement theta. M1=M2=-k*x I know that...

I was confused by how to work this problem in a rotating frame. The solution read that the centrifugal force on the mass should be of magnitude 𝑚𝑤𝑅^2. However, I thought it would be 𝑚𝑤𝐿^2 where L is the distance between the mass and the center of the circle (L = l + R). What am I missing here?

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 :

In problem 1 I assumed that the suspension moves up and down in an oscillating manner, so ##y_0(t)=Acos(\omega t)## I am not quite sure about task 2, but I would say you can remove the motion of the suspension and the motion of the system would not change noticeably, as I assume that the...