For a simple pendulum of length l, the angle theta between rest position and deflected position is the only generalized coordinate. Kinetic energy of the bob of mass m is T = 1/2 ml2 theta prime2, and its potential energy, V = mgl (1- Cos theta). Display the Lagrangian, L of this system, and hence determine the equation of motion for the simple harmonic motion for the smal angle theta.

For a simple pendulum of length l, the angle theta between rest position and deflected position is the only generalized coordinate. Kinetic energy of the bob of mass m is T = 1/2 ml2 theta prime2, and its potential energy, V = mgl (1- Cos theta). Display the Lagrangian, L of this system, and hence determine the equation of motion for the simple harmonic motion for the smal angle theta.

Related questions

Q: Find the Lagrangian and Lagrange's equations for a simple pendulum if the cord is replaced by a…

A: Spring constant of spring = k If unstretched the spring length is r0.The potential energy of the…

Q: A mass-spring-dashpot system has mass m = 2 kg, spring constant k = 9 N/m, and drag coefficient c =…

Q: 3. The motion of a mass-spring system with damping is governed by y"(t) +by' (1) + 16y(t) = 0; y(0)…

Q: There is a pendulum in an elevator going down with constant velocity v. Assuming the mass of the…

Q: Let us say we have a rod with the length (L) and the mass (M) that is pivoted at its middle. This…

Q: x(t) = . which means the system is (Use integers or decimals for any numbers in the expression.…

Q: A particle of mass m is suspended from a support by a light string of length which passes through a…

Q: (a) For this motion, find the amplitude. (b) For this motion, find the period. (c) For this…

Q: Determine the vector field associated with the first-order system specified.(b)Sketch enough vectors…

Q: Suppose that a mass is initially at X = Xo with an initial velocity Vo. Show that the resulting…

Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the…

Q: Coupled Flarmonic Oscillators X2 : 0 ) Write down the 2nd law for each of the masses. Use…

A: We will only answer the first question since the exact question to be answered was not specified.…

Q: In the following vibration system, disk 2 rolls on a non-slip part with uniform mass distribution…

A: Given data, Mass of each component = m Spring constant of the spring = k

Q: By using hamiltonian equations. Find the solution of harmonic oscillator in : A-2 Dimensions B-3…

A: For a Harmonic oscillator, the Kinetic energy T and Potential Energy V are given by, Considering…

Q: A particle of mass moves in a 2-dimensional plane under the influence of a force spring (in figure)…

A: Given a particle of mass say is moving under the influence of a force with initial position position…

Q: Find the steady state solution of the forced Mass-Spring-Damper with the following parameters…

Q: A cylindrical disc with a mass of 0.619 kg and radius of 0.575 m, is positioned such that it will…

A: We are given simple harmonic motion of a physical pendulum. We have used a cylinder here. We first…

Q: Consider the block of mass m, connected to a spring of spring constant k and placed on a inclined…

A: Given:- (1) A block of mass m moves on a plane = 2 N - K Here, N = 1 k = 0 (constraints)…

Question

For a simple pendulum of length l, the angle theta between rest position and deflected position is the only generalized coordinate. Kinetic energy of the bob of mass m is T = 1/2 ml² theta prime², and its potential energy, V = mgl (1- Cos theta). Display the Lagrangian, L of this system, and hence determine the equation of motion for the simple harmonic motion for the smal angle theta.

Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Please, I want to solve the question correctly, clearly and concisely
My system is a pendulum attached to moving horizontal mass m_1 and the pendulum m_2 that is shifted by X_o from origin. I have the lagrangian of my system what would be my equations of motions in terms of small angle approximation and what’s is their frequency?
one-dimensional crystal assembled from three identical atoms connected to one another and to the walls by identical springs as shown.find the normal modes of given system.plot relative displacements versus time for all three normal modes.
The system in the figure below is in equilibrium, and its free body diagram drawn on the right. The distance, d is 1.14 m and each of the identical spring's relaxed length is l0 = 0.57 m. The mass, m of 0.86 kg brings the point P down to a height h = 15 cm. The mass of the springs are negligible. Calculate the following quantities: (a) The angle ? (b) The force exerted on P by the right spring (c) The force exerted on P by the left spring (d) The total spring length (e) The stretch length (f) The stiffness constant of the springs
Develop a Lagrangian for the double pendulum. You may need to make some assumptions to simplify the problem. You may also need to introduce some new variables to make the problem work. Make sure that is explained.