MATH 0290 Midterm: Math 0290 Exam 1 (0290) 2015 Fall Solution -183
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S o l u t i o n s: (10 points) a 0. 25 kg mass is attached to a spring having a spring constant 9 kg/s2. The system is displaced 0. 3 m from its equilibrium position and released from rest. If there is no dumping present, nd the amplitude, frequency, and phase angle of the resulting motion. 0. 25x + 9x = 0, x(0) = 0. 3, x (0) = 0. After multiplication the equation by 4 we get. The natural frequency is 0 = 36 = 6 and the general solution is x(t) = c1 cos 6t + c2 sin 6t. Then x (t) = 6c1 sin 6t + 6c2 cos 6t. The initial conditions give x(0) = c1 = 0. 3, x (0) = 6c2 = 0, c2 = 0. x + 36x = 0. The amplitude is 0. 3, frequency is 6, and phase angle is 0. (the angle is 6 rad/sec or 6/2 = 3/ hz).
