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Consider the case of a one-dimensional harmonic oscillator on the x-axis. Determine the Hamiltonian of the system using the Lagrangian transformation, then determine the equation of motion!
The Hamiltonian of a system is given in the form of the equation H = 1/2 (1/q^2 + p^2 q^4)
Write down the equation of motion for q !
Consider the case of a triple pendulum with the same mass and length of string, m1 = m2 = m3 = m and l1 = l2 = l3 = l. If the angles of deviation are 1, 2, and 3, respectively, determine the equation of motion for the system!
A uniform solid ball of mass m and radius r rolls down an inclined plane with an angle of inclination . Determine the equation of motion using the Hamiltonian
A pendulum of mass m is suspended from a block of mass M which is free to move only
in the horizontal direction only. If the pendulum is free to move only in the XY plane, find the acceleration
the system uses Lagrangian!
A uniform solid ball of mass m and radius r rolls down an inclined plane with an angle of inclination . Determine the equation of motion using the Hamiltonian
Two block of equal mass m are connected by a flexible cord. One block is placed on a smooth
horizontal table, the other block hangs over the edge. Use the Lagrangian to find the acceleration of
the system assuming the cord is heavy of mass m’!
A system comprising blocks, a light frictionless pulley, a frictionless incline at 30°, and a rope connecting 6.0-kg and 4.0-kg blocks on the incline with the 6.0-kg block being lower than the 4.0-kg block. The rope extends to a 9.0-kg block. The 9.0-kg block hangs over the pulley on the side of the incline and accelerates downward when the system is released from rest. The tension in the rope connecting the 6.0-kg block and the 4.0-kg block is closest to
- A. 30 N.
- B. 39 N.
- C. 36 N.
- D. 42 N.
- A car traveling 36km/hr accelerates uniformly at 2m/s.calculate the velocity after 5s
A tower has built by placing many rough books one on another(like a coin tower). The coefficient of friction between each book is μ. What is the minimum force required to pull out the n-th book from the top a little bit out while keeping all other books stationary(non-moving)?
