Q. 4 Simple pendulum has a bob of mosing Suppert (pendulm wih maing Suppert) the massm at the which mores ona horizondd line in Vertical plane in which the pendulum and oscillater Find the Lagrangian Lagrange's eguation of Motion. mi

Q: A particle is suspended from a point A by an inextensible string of length L. It is projected from B…

A: (a) Using Newton's law, W+T=ma

Q: A coupled pendulum system is in a vertical plane (as shown in the fig. 2). Each rod is of nass m and…

A: Concept- Considering two rods which are connected together by a spring that are connected at middle…

Q: (a) Show that the transformation Q = p + iaq, P = (p − iaq) / (2ia) is canonical and find a…

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Q: you know that the escilator drops to 1/5 of its initial values after using it from the full…

A: It is known that the waning frequency is calculated as, ωd=ωn1-ζ2, where ωn is the natural…

Q: . A particle of mass m in 3D is subject to a potential V(x, y, z) = ²x Write the Lagrangian and the…

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

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Q: Consider a particle of mass m moving in the following potential V(x)= vị for xv2. What is the grown…

A: The potential is specified as: Vx=v1 for x<0Vx=0 for 0≤x≤aVx=v2 for a<x≤aVx=∞ for x<2a…

Q: Q Calculate the velocity of longitudinal and shear elastic waves in a cubical crystal along (111)…

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Q: The Longrongion of 1D harmonic oscilator is, () write Euler-Congrange equation of system? ().write…

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Q: 4.5 In aerodynamics and fluid mechanics, the functions u(x,y) and v(x,y) in f(z) = u(x,y) + i v(x,…

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Q: Obtain the value of the Lagrange multiplier for the particle above the bowl given by x^2+y^2=az

A: To find the Lagrange multiplier for the particle above the bowl defined by x2+y2=az, we need to set…

Q: Find a Lagrangian corresponding to the following Hamiltonian: H = (P4 + 2P.P. + i)

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Q: A simple pendulum of mass m and length L is shown in the figure below. Take the reference of…

A: Part (a) The given pendulum is constrained to move in the XY plane only. Hence z coordinate of the…

Q: q mass m. movesS in ene dimension Such that it has Lograngian the 12 ere v is differentiable…

A: Euler Lagrangian equation is given byL= m2x2.12+mx2 v(x)-v2(x). we have…

Q: Q2: A pendulum bob of mast m is suspended by a string of length / from a car of mass M which moves…

A: To determine: (a) The Lagrangian function  The mass of the pendulum is m, the length of the pendulum…

Q: (Hour29) Find parametric equations and a parameter interval for the motion of a particle that moves…

A: Given: y = x2 points:  (0,0) to (2,4) then (2,4) to (-2,4) To Find: parametric equation

Q: Consider a Critically damped oscillater of m, damping 4ficient b, mas Co- Dand initial displadementA…

A: The energy of a damped oscillator is given by :  E=12kAe-b2mt2Here, A is amplitude of oscillation…

Q: There is a pendulum wth a length of 13.9me ters. suings with En amplitude of O. 088 meters, what is…

A: maximum acceleration(amax) of the pendulum.given,Amplitude(A)=0.088 mlength of pendulum(L)=13.9…

Q: Lagrangian of a particle is L--m(r² +r*ö* )-r (r).Which of the following options 71. is correct ?…

A: Lagrangian is given by:

Q: Q4) Find the natural frequencies of the system below (without using lagrange or energy equations).…

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Q: O A Simple Harmonic oscillator of mass m and natural freguency Wo, driving 4t)- maloscot .…

A: Given condition at t=o,  The given differential equation The solution of this equation is sum of…

Q: 3.1 Given the force field F=(4xy – 3x'z*)î +(4y+2x*)j+(1–2x'z)& 3.1.1 Prove that Fo dr is…

A: Solution: 3.1.1. The given integral will be independent of, c if the force is conservative. A force…

Q: Find the lagrangian nd eqution of motion for double pendulum where l1and l2 are the lengths of…

A: Let us consider the point O as the origin.

Q: The Lagrangian for a one-dimensional harmonic oscillator is (a) kx 1 (b) mx2 (c) mx+ kx (d) mx + kx-

A: Here, we use the formula of Lagrangian to get the required.

Q: Lagrangian of a system is +2?) +2mo(xỳ – yử)+ mo² (x² + y²) what x component of force on the system.

A: Given: The lagrangian of the system is L=12mx˙2+y˙2+z˙2+2mωxy˙-yx˙+mω2x2+y2. The equation of…

Q: If the particle has a velocity vo = 5 mm/s at t = 0, determine the particle position, velocity, and…

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Q: Show that the minimum energy of a simple harmonic oscillator is hω/2. What is the minimum energy in…

A: The mean value of x2av is the mean square devation ∆x2By substituting the mean square deviation…

Q: A block with a mass of the spring, whose mass is neglected and the spring constant given in the…

A: Solution: a) Let M be the mass of the block attached to the spring of spring constant k. The…

Q: With what velocity vo should a projectile be started at the center of the Earth to reach the surface…

A: As per the guidelines we can solve only 1 question. Solution of 1st question is given Law of…

Q: 43. The pnrabolic coordinates (.n) are related to the Cartesian coordinate (x, y) by x = En and y…

A: Given: x=ξηy=ξ2-η2

Q: Work out the force due to the Miyamoto-Nagai disc potential.

A: Miyamoto – Nagai model provide potential for disks with a finite thickness so he modify Kuzmin model…

Q: Calculate the reflection coefficient R and the transmission coefficient T of the scattering caused…

A: Answer

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: Question Four: For the simple pendulum Shown: If the string is an elastic one with elastic (force…

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Q: Derive and discuss the Lagrange equation of motion of a of radius ca? body maving on a sphere

A: Given: The radius of the sphere is a. Introduction: The Euler equation is a second-order partial…

Q: A pendulum hangs from a fixed point, but the pendulum itself is a spring with a constant k and…

A: A pendulum which is a spring hangs from fixed point is as shown in the following figure. Since the…

Q: A double pendulum consists of two equal masses 'm' suspended by two strings of length L. What is the…

A: Solution: The free-body diagram is

Q: For a simple pendulum of length l, the angle theta between rest position and deflected position is…

A: Given that:T=12ml2θ˙2V=mgl1-cosθLagrangian  of the system is given as:L=T-VL=12ml2θ˙2-mgl(1-cosθ)

Q: write oniy he normalization and orthogonal conditions of the set of wavefunctions Y, and Y , using…

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