Pendulum Definition and 1000 Threads

When we have solid rod instead of spring I can solve this problem in Microsoft Excel either with Euler´s method or Runge Kutta method, but that spring makes this problem hard for me.

Hi, I would like to ask what is the formula for non-harmonic oscillation of pendulum? I know that formula for harmonic oscillation of pendulum is: (d^2 φ)/(dt^2 )+g/r sinφ=0 where φ is angle, t is time, g is gravitational acceleration, r is length of a rope. I know that harmonic oscillation...

Homework Statement A simple pendulum is formed by a light string of length ##l## and with a small bob ##B## of mass ##m## at one end. The strings hang from a fixed point at another end. The string makes an angle ##\theta## with the vertical at time ##t##. Write down an equation of motion of...

Hello, I was solving a problem related to Eddie currents recently and I need some help with simulating it numerically. Basically, we have a disc-like copper pendulum entering a region of uniform magnetic flux density B (see diagram). I understand that I need to use Faraday's law: \nabla...

1. Homework Statement Hey guys, I am reading my Physics book, in that specific section it says "the restoring force must be directly proportional to x or (because x=(theta)*L) to theta" Homework Equations The Attempt at a Solution I have tried to look for that x=(theta)*L relationship...

I have encountered two separate review problems that have to do with finding a value for amplitude and I am really struggling with it. 1. Homework Statement Question 1- A mass of 3kg is free to move on a horizontal frictionless surface and attached to a spring of k=15 N/m. It is displaced...

<Mentor's note: moved from a technical forum and thus no template.> A pendulum consists of a bob of mass M and a rigid rod of length ℓ with negligible mass. The bob is struck by a bullet of mass m. The bullet passes through the bob and emerges with a speed half that of impact. The shot causes...

Homework Statement I'm writing a small project as part of my degree, and I am stuck on proving one (probably simple!) thing towards the end. I've shown that the pendulum is periodic and has a total period of 4t2. Homework Equations [/B] The Attempt at a Solution I think I need to...

Homework Statement The drawing shows three situations in which a block is attached to a spring. The position labeled "0 m" represents the unstrained position of the spring. The block is moved from an initial position x0 to a final position xf, the magnitude of the displacement being denoted by...

Homework Statement I am investigating a scenario where a pendulum with a bob attached is released from an angle and pushes a box to a certain distance. My goal is to find the coefficient of friction between the box and the surface it moved on. I have measurements for: - mass of the bob (125...

Homework Statement This problem deals with a pendulum. Imagine you're just letting it dangle (so perpendicular to ground) and you lift it to the side by some angle theta. This point your holding it at will be Point A. You release the pendulum from your grip and want to find out at Point B...

Homework Statement Video was recorded with a 240 fps camera. It took 93 frames for the pendulum to go from 90 deg to the bottom. The pendulum length is 51 cm. Homework Equations Find the max velocity The Attempt at a Solution From the simple pendulum equation, I should get around 11.36 km/hr...

Homework Statement A pendulum of length l at the north pole is moving in a circle to the east at an angle \theta to the vertical. It has some period T_E as measured in the rotating Earth frame. The experiment is then repeated except now the pendulum is moving to the west with period T_W...

Homework Statement I have to calculate the propagated error on g of pendulum. I pretty much measured the T of pendulum and now calculating g while increasing the number of cycles. Homework Equations I used the equation of propagated error and i included picture of it and my calculations. The...

Homework Statement Hi guys I am having a problem deriving this solution for a simply pendulum. Could someone please help me. My issue is taking the second order and getting into just cos. I have attempted a solution which is shown below. Homework EquationsThe Attempt at a Solution...

Homework Statement A pendulum obeys the equation \ddot{\theta} = -\sin(\theta) and has amplitude \theta_0 . I have to show that the period is T = 4 \int_{0}^{\frac{\pi}{2}} \frac{d\phi}{\sqrt{1-\alpha \sin^2(\phi)}} where \alpha = \sin^2(\frac{\theta_0}{2}) 2. The attempt at a solution...

Homework Statement To find the period of oscillation of the pendulum and the equation of motion. Homework Equations Conservation of energy. Potential energy in a constant field = mgh. Kinetic energy in polar coordinates with r constant = (1/2) m r2 (dΘ2/dt2) The Attempt at a Solution I won't...

I find it somehow confusing to imagine why m*a=-k*x is "generally valid". that minus sign bothers me. Imagine I raised a bob to some height (ex. from the left side) and then released it. from that moment till the moment where it reaches equilibrium position m*a and restoring force have same...

1. Homework Statement i was solving the 2008 semi final us physics olympiad paper when i got stuck on question B2 in part 2 http://www.aapt.org/Programs/contests/upload/olympiad_2008_semi-final_soln.pdf the link takes you a pdf with questions and solution however i don't understand the soution...

Hello! I try to think about the Foucault pendulum with the concept of parallel transport(if we think of Earth as being a perfect sphere) but I can't quite figure out what the vector that gets parallel transported represents(for example, is it the normal to the plane of oscillation vector?). In...

Scenario There is a pendulum suspended on an arm that rotates a certain angle in the horizontal plane. The arm suddenly stops, how far will the mass of the pendulum be displaced in the horizontaly? Thought so far: The momentum of the arm will be L=IW and when it stops I think the mass at the...

Hi, I'm trying to program a simple physics engine from scratch as an exercise, and I'm starting with manipulating a stick with the mouse pointer. As of now, it dangles from one end demonstrating simple pendulum physics. Now, I want to add a friction component to the "axle" it's rotating on to...

1. The problem statement, all variables and given/knowns So basically,I am confused by this quote in David Morin's Problems and Solutions in Introductory Mechanics that says: the tension in the tilted string has a nonzero horizontal component (except at the highest points where the tension is...

Homework Statement A tether ball of mass ##m## is suspended by a rope of length ##L## from the top of a pole. A youngster gives it a whack so that it moves with some speed ##v## in a circle of radius ##r = L sin(\theta) < L## around the pole. a) Find an expression for the tension ##T## in the...

Homework Statement Finding the equation for the muzzle velocity by using conservation of energy. 2. The attempt at a solution Ek+Eg=Ek2+Eg2 Well I'm 100% sure the kinetic energy of the ball is transferred into the catcher. The displacement is 1.9cm which is 0.019m. Mb=0.0077Kg (mass of ball)...

Homework Statement A .01kg bullet is fired into a 1.2kg block hanging from a 1m wire. The bullet exits the block with a speed of 200m/s and the block swings to a height of .2 meters. What is the original velocity of the bullet? What percentage of the original energy of the bullet is no longer...

Usually, the pendulum problems I encounter relate to initial velocity. What happens if, at equilibrium, I push a pendulum with a certain amount of force? (E.g. 10N) Is there a way to calculate how high the pendulum will go? I guess it's complicated considering torque done by gravity, etc

(This is NOT a homework problem. It's an engineering problem I'm trying to crack.) A wheel with a rubber tire (friction) can roll on a suspended rail. Attached to it is a pendulum that's rigidly mounted on the axle of the wheel with a mass that can hand down and swing. (The wheel's rotation...

If a pendulum consisting of a string and a bob is allowed to swing in a vacuum vs in air, which has larger period?

Homework Statement you are taking your pendulum clock with you to a visit of the Jupiter moon Io(radious 3643.2Km, mass 8.94X10^22 kg. calculate the duration of a full Oscillation. On the surface this oscillation time was 1s Homework Equations T=2*π√l/g[/B]The Attempt at a Solution T1/T2=√(g2/g1)

I have done an experiment changing the mass ratio of coupled pendulums. To conclude I need real world applications for the coupled pendulums. But, i cannot find it online. So, it would be really helpful is someone could give examples of this. THANKS!

In my problem the linear modal is defined as the first term in the series expansion of \sin(x) so: \sin(x) = x - \frac{x^{3}}{3!}+\dots \sin(x) = x is the linear modal. So with this, I then have to write \frac{d^{2}x}{dt^{2}} = -\sin(x) as a system of x^{\prime} and y^{\prime}, so...

So say a pendulum consisting of a non rigid string and mass bob is swung above the horizontal position. It's given an impulse at the bottom so that in the swing, there is nothing but tension and gravity acting. At above the horizontal, the gravity is pointing down while the tension can only...

I've got an accelerometer swinging back and forth on a string collecting data. But because of the tolerance of the accelerometer, the data is not quite clean enough to simply determine when positive turns to negative, or passes through equilibrium. Here's the data. (arbitrary reading vs. time...

Homework Statement Homework Equations The Attempt at a Solution Working with equation 18.1 i found that However, this obviously is not the equation in 18.3. I found a source talking about this problem, and they get a similar equation http://file.scirp.org/pdf/JAMP_2014031310562629.pdf I...

Homework Statement A pendulum with a mass m hanging on a elastic bug rigid massless rod which may swing in the xy-plane. The pivot point is the origin of the coordinate system. The force acting on the pendulum is the sum of force of an elastic central force directed towards the origin, and...

Homework Statement a pendulum of mass m and length L is pulled back an angle of θ and released. After the pendulum swings through its lowest point it encounters a peg α degrees out and r meters from the top of the string. The mass swings up about the peg until the string becomes slack with the...

Homework Statement A steel ball of mass 0.890 kg is fastened to a cord that is 50.0 cm long and fixed at the far end. The ball is then released when the cord is horizontal, as shown in the figure. At the bottom of its path, the ball strikes a 2.50 kg steel block initially at rest on a...

(I apologise if this is the wrong area to post) Hello everybody I am planning on building my first Focault Pendulum(As a physics projject for school) and I have a few questions. I am going to purchase a cable(it needs to be smooth and friction-less around 7 feet), I also am going to need to...

<< Mentor Note -- OP correctly re-posted schoolwork question in the HH forums; threads merged >> The full question is: The pendulum inside a grandfather clock has a half period of 1.0000s at a location where the magnitude of the local acceleration of gravity is 9.800 m/s^2. The clock carefully...

Hi all! I've come here to seek your expertise because I've ran into a bit of a heated discussion (well, heated from the other side ;-) about rockets, hovering and center of gravity. Basically people are referencing to the pendulum fallacy when I say that a rocket which is hovering would be...

Homework Statement A monkey is swinging a coconut of 1 k in a pendulum like motion. When the monkey's motion is at the bottom of its swing it is .6 m above the ground. He releases the coconut when it it is in this position when the force is 250 N and it travels 10 meters before hitting the...

Homework Statement This isn't a specific problem, I just wondering if there was a formula to describe the direction of travel an object would take if it was part of a pendulum and the string broke. Homework EquationsThe Attempt at a Solution Seeing that if the string broke in the instant that...

Homework Statement So we had to the simple pendulum experiment and were measuring the effect of the length of the pendulum on its period of motion. However, our results produced a line of best fit that was significantly higher than the expected line of best fit (with length vs period squared)...

Homework Statement Find the Lagrangian for the double pendulum system given below, where the length of the massless, frictionless and non-extendable wire attaching m_1 is l. m_2 is attached to m_1 through a massless spring of constant k and length r. The spring may only stretch in the m_1-m_2...

Homework Statement A mass is suspended from a crane by a cable of length L. The crane and the mass is moving at constant speed V. The crane stops and the mass on the cable swings out. What is the angle that the mass swings? If the angle is 50 degrees and L=6m, what is the initial speed of the...

I am trying to derive an expression for the Tension T in the massless bar in the given photo. Where there is a cart that is moving only in the x-direction and the bar is rotating around a point pivoted at the cart with angle theta. The expression that I have is deduced from: ∑ F (towards...

Hello, I'm trying to develop a pendulum to test protective equipment so I want to work out the length I'll need to generate a desired velocity and the necessary mass I'll need for a specific moment of inertia. I know there are multiple ways to solve for linear velocity with equating Ek and Ep...

Is this a legitimate equation? θ'' = − g⁄R sin θ Source: ftp://www.myphysicslab.com/pendulum1.html ftp://www.myphysicslab.com/images/pendulum_2.gif The pendulum is modeled as a point mass at the end of a massless rod. We define the following variables: θ = angle of pendulum (0=vertical) R =...

Homework Statement Find the large oscillation period T of pendulum. Suppose that the amplitude is ##\theta_0## We can write oscillation period T by the sum of a series, know that: $$\int_0^1 \frac{dt}{\sqrt{(1-t^2)(1-k^2t^2)}}=\frac{\pi}{2} \sum_{n=0}^{∞}(\frac{(2n)!}{2^{2n}(n!)^2})^2$$ Let...