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midterm1 sol - Midterm 1 Physics 1B Name ID number Lecture...

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Midterm 1 Physics 1B —————————————————— Name: —————————————————— ID number: —————————————————— Lecture 1 Section (A-F): —————————————————— 1. Three identical springs with the spring constant k = 100 N/m are connected as shown in the figure. Neglecting the friction, calculate the period of oscillations of the mass m = 6 kg. m k k k Solution. A displacement x causes each of the springs on the left-hand side to compress by ( x/ 2). Because the two springs are in series, they produce equal forces: F 1 = F 2 = - k x 2 . Meanwhile, the spring on the right acts with force F 3 = - kx. The net returning force is, therefore, F net = - k x 2 - kx = - 3 k 2 x = - k eff x, where k eff = 3 k 2 . The period of oscillations T = 2 π s m k eff = 2 π s 2 m 3 k = 1 s 1
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2. The two weights, m 1 = 1 kg and m 2 = 2 kg hang on the spring as shown in the figure. Ini- tially the system is in equilibrium, and the weights are at rest. When the string connect-
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