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A vertical spring with a fixed upper end and constant 1.6 N /m has a 400 g object suspended at its lower end. An external force acts numerically on the weight, in newtons equal to F (t) = 2 sin (2t), with a positive downward direction. Initially the weight is 15 cm below the equilibrium position and is thrown with an initial upward velocity of 1.2 m / s. If the damping force is negligible: (a) Write the differential equation associated with the problem and its initial conditions. mx'+ Kx =2 sin (24) Xg = 0,15 m xo =1,2m/S (b) Determine the position of the object at any time t. (c) Indicate whether this system enters mechanical resonance. Justify,
Transcribed Image Text:A vertical spring with a fixed upper end and constant 1.6 N /m has a 400 g object suspended at its lower end. An external force acts numerically on the weight, in newtons equal to F (t) = 2 sin (2t), with a positive downward direction. Initially the weight is 15 cm below the equilibrium position and is thrown with an initial upward velocity of 1.2 m / s. If the damping force is negligible: (a) Write the differential equation associated with the problem and its initial conditions. mx'+ Kx =2 sin (24) Xg = 0,15 m xo =1,2m/S (b) Determine the position of the object at any time t. (c) Indicate whether this system enters mechanical resonance. Justify,
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