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10 Nov 2019
A block of mass M is connected to a spring of mass m and oscillatesin simple harmonic motion on a horizontal, frictionless track(Figure P15.62). The force constant of the spring is k and theequilibrium length is l. Assume that all portions of the springoscillate in phase and that the velocity of a segment dx isproportional to the distance x from the fixed end; that is, vx =(x/)v. Also, note that the mass of a segment of the spring is dm =(m/)dx.
(a) Find the kinetic energy of the system when the block has aspeed v. (Use M, m, and v as necessary.)
(b) Find the period of oscillation. (Use M, m, and k as necessary.)
A block of mass M is connected to a spring of mass m and oscillatesin simple harmonic motion on a horizontal, frictionless track(Figure P15.62). The force constant of the spring is k and theequilibrium length is l. Assume that all portions of the springoscillate in phase and that the velocity of a segment dx isproportional to the distance x from the fixed end; that is, vx =(x/)v. Also, note that the mass of a segment of the spring is dm =(m/)dx.
(a) Find the kinetic energy of the system when the block has aspeed v. (Use M, m, and v as necessary.)
(b) Find the period of oscillation. (Use M, m, and k as necessary.)
Tod ThielLv2
25 Apr 2019
