3. A pendulum consist of a mass m suspended by a massless spring with natural length ro and spring constant k. (i) Sketch the system and determine the generalized coordinate. (ii) Calculate the Lagrangian, L = L(qk» qk). (ii) Calculate the generalized momenta for each generalized coordinate. (iv) Determine the Hamiltonian H = H(qk, Pk). (v) Determine the Hamilton's canonical equations of motion and show that %3D İk = [9r,H], and pg = [Px, H] %3D for each generalized coordinate and [,] denotes Poisson bracket.
3. A pendulum consist of a mass m suspended by a massless spring with natural length ro and spring constant k. (i) Sketch the system and determine the generalized coordinate. (ii) Calculate the Lagrangian, L = L(qk» qk). (ii) Calculate the generalized momenta for each generalized coordinate. (iv) Determine the Hamiltonian H = H(qk, Pk). (v) Determine the Hamilton's canonical equations of motion and show that %3D İk = [9r,H], and pg = [Px, H] %3D for each generalized coordinate and [,] denotes Poisson bracket.
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![3. A pendulum consist of a mass m suspended by a massless spring with natural
length ro and spring constant k.
(i) Sketch the system and determine the generalized coordinate.
(ii) Calculate the Lagrangian, L =
(iii) Calculate the generalized momenta for each generalized coordinate.
(iv) Determine the Hamiltonian H
(v) Determine the Hamilton's canonical equations of motion and show that
H(qk, Pk).
%3D
İk = [qx,H],
and pg = [Pk, H]
%3D
%3D
for each generalized coordinate and [,] denotes Poisson bracket.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42fa9a1d-cfe5-48ae-96e5-4f7230a5ca71%2Fa76ee7ff-6a93-48a1-8e45-6d4f75a9d9a1%2Ftu88dwe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. A pendulum consist of a mass m suspended by a massless spring with natural
length ro and spring constant k.
(i) Sketch the system and determine the generalized coordinate.
(ii) Calculate the Lagrangian, L =
(iii) Calculate the generalized momenta for each generalized coordinate.
(iv) Determine the Hamiltonian H
(v) Determine the Hamilton's canonical equations of motion and show that
H(qk, Pk).
%3D
İk = [qx,H],
and pg = [Pk, H]
%3D
%3D
for each generalized coordinate and [,] denotes Poisson bracket.
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