A horizontal spring-mass system has low friction, spring stiffness 200 N/m, and

Question

A horizontal spring-mass system has low friction, spring stiffness 200 N/m, and mass 0.4 kg. The system is released with an initial compression of the spring of 11 cm and an initial speed of the mass of 3 m/s. (a) What is the maximum stretch during the motion? m (b) What is the maximum speed during the motion? m/s (c) Now suppose that there is energy dissipation of 0.03 J per cycle of the spring-mass system. What is the average power input in watts required to maintain a steady oscillation? watt

Explanation / Answer

? = ? (k/m) = ? (200/0.4) = 22.36 rad/s......... x = A sin (? t + ?) and v = A ? cos (? t + ?)............ At t = 0, v = 3m/s......... 3= A 22.36 cos ?) -----------1 At t = 0, x = 0.11m............ 0.11= A sin ?------------------------2......... tan ? = 0.11*22.36/3 ? = 39.34? --------------------------------------

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