A heavy particle is placed at the top of a vertical hoop. Calculate the reaction of the hoop on the particle by means of the Lagrange's undetermined multipliers and Lagrange's equations. Find the height at which the particle falls off.

Q: (3) Consider the Hamiltonian given as H = +²+Fâ , where each term has a clear physical meaning. 2m 2…

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Q: Show that the equation * + 2ßx + wžx = 0 can also be obtained from the following modified Lagrange…

A: For harmonic oscillator  Fundamental frequency = √k/m And damping coefficient = b/2m

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Q: Yo STANDART FORM [4+h+ m,r} + m>q} 0 M(q) = m [4,(m,r +m>q;) cos q1 a„m2 sinqi g(q) = l. m, ,I a,

A: In classical mechanics as we know the 2nd order differential equation having a perticular stationary…

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Q: A particle of mass m oscillates in a vertical plane suspended by a massless string that goes through…

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Q: Problem 10.10 Consider a central force given by F(r) = -K/r³ with K > 0. Plot the effective…

A: F= -K/r³ We know that, F= -dU/dr     (where U is  potential energy) -K/r³= -dU/dr dU= K(1/r³)dr…

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A: Since given that Hamiltonian is time dependent then then energy is not conserved.

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Q: If the kinetic energy T and the potential energy V of a mathematical system are given T = (k+;) i +…

A: The Lagrangian function is given by, L = T - V The Hamiltonian function is given by, Hq, p, t =…

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Q: Yo m l. m, ,1

A: In classical mechanics as we know the 2nd order differential equation having a perticular stationary…