Pendulum Definition and 1000 Threads

When I solve this problem i have the equation: $$x''+Asinx=0$$ How solve this equation if x large? I think we use some approximations

Homework Statement Find the Lagrangian and equations of motion for a spherical pendulum Homework Equations L=T-U and Lagrange's Equation The Attempt at a Solution [/B] I found the Lagrangian to be L = 0.5*m*l2(ω2+Ω2sin2(θ)) - mgl*cos(θ) where l is the length of the rod, ω is (theta dot)...

When the pendulum in Problem 3.8 is vibrating freely in unforced oscillation, the amplitude of its swing decreases by a factor of e after 75 cycles of oscillation. (a) Determine the Q-value of the pendulum. (b) The point of suspension of the pendulum is moved according to ξ = a cos ωt at the...

Hi, I was wondering if someone could please help me to understand : 1) How can I prove that a Pendulum is following SHM? 2) Also, does being isochronous also mean that the pendulum is following SHM? Thank You very much.

Hello everyone. In the 3rd edition of Mechanics by Landau and Lifshitz, paragraph 14, there is a problem concerning spherical pendulum. Calculations leading to the integral $$ t=\int \frac {d \Theta} {\sqrt{\frac{2}{ml^2}[E-U_{ef}(\Theta)]}},$$ $$...

Homework Statement Consider the pendulum depicted in the adjacent figure: a mass m is attached to non stretching chord of length `. Directly below the pendulum is a circular disc rotating with constant angular velocity w. We attach to the disk a frame whose x-axis is in the plane of the...

Homework Statement How would one show that the average total energy of a simple pendulum is equal to twice the average kinetic energy of the pendulum? Homework Equations E = T + V = 1/2 ml**2 (θ'**2) + mgl cos(θ) The Attempt at a Solution Maybe use equipartition?

Homework Statement A pendulum is made of a bob dangling from a lightweight string of length ℓ. The bob is pulled sideways so that the string makes an angle θi with respect to the vertical, then released. As it swings down, what is the rotational speed of the bob as a function of the changing...

Homework Statement A rigib poll of length 2L is made into a V shape so that each leg has length L. What is the period of oscillation for small angle. The angle between the legs is 120 degrees Homework Equations 3. The Attempt at a Solution [/B] I tried to calculate the period by imagining a...

Homework Statement The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by T = 2π ℓ/g where ℓ is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show...

Homework Statement What is the ratio between maximum acceleration of pendulum oscillation and the gravity acceleration ? Express the answer in terms of L (the length of pendulum string) Homework Equations SHM The Attempt at a Solution amax = ω2 A = (g/l) L sin θ = g sin θ So, the ratio is...

Homework Statement I have to derive equation of motion for this system. I want to use a moment of force, but i have a problem with moment of force spring. Homework Equations The Attempt at a Solution What I've done is: M(Fg)=-mgLsinα M(N)=0 M(Fb)=mω^2 Lsinα*Lcosα mL^2*α''=ΣM M(Fs)=?

Hi everybody! I have a quick question about a pendulum. The first question of a problem asked me to find an integral expression for the time period of a pendulum without the small angle approximation, which I did and I got that: ##T(\varphi) = 4\sqrt{\frac{l}{g}} \int_{0}^{\pi/2}...

Homework Statement Hi everybody! While preparing my next experiment (Kater's pendulum), I was given for homework to derive an equation to correct the buoyancy when calculating ##g##. I am given the result: ##g_c = (\frac{2 \pi}{T(\varphi_0)})^2 l_r (1 + \frac{\varphi_0^2}{8} +...

Ok, I'm reading up on Lagrangian mechanics, and there is a problem that I don't really understand: the double pendulum (in this case, without a gravitational field). So, I want to take it step by step to make sure I understand all of it. We've got a pendulum (1) with a weight mass m=1kg...

Homework Statement Please see attached image :) Homework Equations Euler-Lagrange Equation \frac{\partial{L}}{\partial{q}} - \frac{d}{dt}\frac{\partial{L}}{\partial{\dot{q}}} = 0 L = T - V The Attempt at a Solution a. The potential energy V is the potential energy from the spring and the...

Homework Statement Hi everybody! I'm back with another lagrangian problem :) Although I think (or hope) I have made progress on the topic, I always learn a lot by posting here! A pendulum with point-shaped mass ##m_1## hangs on a massless string of length ##l##. The suspension point (also a...

Homework Statement Homework Equations T= 2pi*sqrt(L/g) The Attempt at a Solution T= 2pi*sqrt(0.325/9.8)=1.14 s That seems like a reasonable answer. [/B]

Homework Statement Homework Equations The Attempt at a Solution

Homework Statement [/B] find the period with only using L (for the long of the rope), R (for the radius), M (for the mass), and G (for the gravity) Homework Equations V=ωR Fcentripetal = ##\frac {MV^2} {R}## Fgravity = MG phytagoras basic trigonometry The Attempt at a Solution [/B] i have...

Homework Statement Hi everybody! As always, I struggle with my special relativity class and here is a new problem I'd like to have some indications about: A masspoint m moves in the x-y-plane under the influence of gravity on a circular path of radius r (see attached pic). Which constraining...

Homework Statement A pendulum consists of a bob of mass A hanging from a string of non-zero mass m. Its maximum displacement is p/4 [whatever that p means, I do not know. the question writers do a poor job of writing questions]. What is true of the tension in the string? 1) It is greatest...

Homework Statement I am supposed to calculate Lyapunov exponent of a damped, driven harmonic oscillator given by ## \ddot{x} + 2\beta \dot{x} + \omega_0^2 x = fcos(\omega t)## Lyapunov exponent is ## \lambda ## in the equation ## \delta x(t) = \delta x_0 e^{\lambda t} ## The attempt at a...

1. Homework Statement The violet sleeve has mass M and is free to move horizontally without friction. The green rod has mass 2M and length L and can rotate around a pivot on the sleeve without friction. At t=0, the rod is in vertical position and is rotating with angular velocity w. What are...

Homework Statement Homework Equations T=2pi√(L/g) The Attempt at a Solution I am just making sure I am doing these right. For the first one, I used the equation to determine the length it would be on Earth. The length I got was g/pi^2 = 0.993 m. I thought that it would have to stay the same...

Homework Statement We have a rod (length L, mass m) suspended at a point whose distance from the center of mass is a. 1) prove that (generally) there exist two values of a (a1, a2) for which the pendulum oscillates with the same period. 2) derive and explain: T = 2\pi\sqrt{\frac{a_1+ a_2}{g}}...

Hi, I am having some trouble with the following question, any help would be appreciated 1. Homework Statement For a simple pendulum, T^2 is directly proportional to the length of the string (L) Why is this not true for a compound pendulum? Homework Equations T= 2pi sqrt(l/g) [/B]The...

Homework Statement m = 1 kg, l = 1 m, theta 1 and 2 are small I want to work out the natural frequencies (2) of this 2 DOF system through taking torques about the fixed point on the ceiling. I've done it using numerous fixed points and just cannot get the right answer.[/B] Homework...

Homework Statement A simple pendulum of length ξ and mass m is suspended from a point on the circumference of a thin massless disc of radius α that rotates with a constant angular velocity ω about its central axis as shown in Figure. Find the equation of motion of the mass m. Homework...

Homework Statement With this problem I have to get the answer: cosθ = r/L * cosα - √(3)/2 * (1 - r/L) which in other words mean I need to find angle θ with arccos[r/L * cosα - √(3)/2 * (1 - r/L)]. Here's the picture: Lcosθ is the vertical length of the string at its lowest point. rcosα is a...

Homework Statement Calculate the Lagrangian of this set up: Imagine having two ropes: They are both attached to the ceiling and have different lengths. One has length b and the other has length 4b. Say they are hooked to the ceiling a distance 4b apart. Now, the ropes are both hooked to a...

I am doing the compound pendulum experiment but I am stuck on how to find the value of g from the graph Here's a description of the compound pendulum: The compound pendulum AB is suspended by passing a knife edge through the first hole. The pendulum is pulled aside through a small angle and...

Homework Statement A ballistic pendulum is a device that may be used to measure the muzzle speed of a bullet. It is composed of a wooden block suspended from a horizontal support by cords attached at each end. A bullet is shot into the block, and as a result of the perfectly inelastic impact...

Homework Statement Hi everyone! Here is a new problem about oscillations! Thx to all of you, I'm definitely making progress in the field. Let's see how that problem goes: A pendulum of mass m is hanging on a string of length L and is "pushed" by a spring with spring constant k. At the deepest...

Homework Statement Hi everybody! Two masses m1 and m2 are connected with a spring one after the other to a wall (see attached picture). The spring constants are k1 and k2. To consider here are only longitudinal oscillations and no external forces. a) Express the Newtonian equations of motion...

Homework Statement A person shakes pendulum with length 3.6 meters. For 12 shakes he measured the time of 38 seconds. Find the acceleration due to gravity Homework Equations T=t/n T=2*pi*sqrt(l/g) The Attempt at a Solution T(period)=t/n=3.167 T=2*pi*sqrt(l/g) l-length g=4*(pi)^2*l/T^2...

Homework Statement A ball of mass m is attached to a string of length L and released from rest at point A. Show that the tension in the string when the ball reaches point B is 3mg, independent of the length l. (there is an image in attachment ) [/B] Homework Equations K = mv2/2 U = mgh Fcp =...

how is a bifilar pendulum useful in everyday life and why do we study about it?

Homework Statement In a thought experiment, a train is moving at a speed of 0.95c relative to the ground. A pendulum attached to the ceiling of the train is set into oscillation. An observer T on the train and an observer G on the ground measure the period of oscillation of the pendulum. State...

http://physics.stackexchange.com/questions/243457/about-the-formula-of-pendulum-simple a(t) = a0 * sin ( sqrt(g/l) * t * Pi/2 ) - [ k/(mll) * cos ( sqrt(g/l) * t * Pi/2 ) * t ) ] a(t) : the angle in instant t . t : time g : gravity . Pi = 3.14 k = Fixed (Friction ) l : longer of pendulum...

Homework Statement Spring connected to a pendulum holding a ballwith mass m, length l, spring constant k, spring deflection x, angle of pendulum alpha, angular velocity w.Homework Equations Derive the angular acceleration The Attempt at a Solution I made the three body diagram, and find that...

Homework Statement Q The length of a simple pendulum executing SHM is increased by 21% .The percentage increase in the time period of the pendulum of increased length is a) 11% b) 21% c)42% d)10% Homework Equations ##T = 2\pi\sqrt{\frac{L}{g}}## The Attempt at a Solution ##T^2 =...

Homework Statement As the captain of the scientific team sent to Planet Physics, one of your tasks is to measure g. You have a long, thin wire labeled 1.80 g/m and a 1.30 kg weight. You have your accurate space cadet chronometer but, unfortunately, you seem to have forgotten a meter stick...

Homework Statement The scenario is a pendulum of length l and mass m2 attached to a mass of m1 which is allowed to slide along the horizontal with no friction. The support mass moves along in the X direction and the pendulum swings through the x-y plane with an angle θ with the vertical. After...

Homework Statement I am studying a question in Marion's classical mechanics: I am successful in obtain the equation of motion, which is where theta is the theta shown in . However, in the second part of the solution, , it puts derivative of theta to be zero and I can't understand this. Also...

Homework Statement How do you find the position of a pendulum as a function of time? Mass of bob: 2.0kg String length (l): 3.0m The pendulum is displaced as a distance of 0.35m from the equilibrium point and is then released. After 100 swings the maximum displacement of the pendulum has been...

Hello I am studying for my exam and found an interesting exercise that I'm trying to solve 1. Homework Statement A pendulum consists of a thin rod of length ℓ and mass m suspended from a pivot ∇ in the figure to the right. The bob is a cube of side L and mass M, attached to the rod so that the...

Homework Statement Mass ##M## hangs from a string of length ##l## which is attached to a rod rotating at constant angular frequency ##\omega##. The mass moves with a steady speed in a circular path of constant radius. Find ##\alpha##, the angle the string makes with the vertical. Homework...

Homework Statement how far from the rim of a disk of Radius R must the pivot point be located in order for its period of oscillation to be a minmum where R is the distance from the point to the centre of mass? I'm stuck at the derivative because I saw a similar problem where the answer is...

Homework Statement Q. What is the time lost in time 't' by a pendulum clock whose actual time period is T and the changed time period at some higher temperature is T' ? (T' is Time period at some higher temperature , l' is the increased length , Δθ is the difference in temperature, α is...