A vertical spring with a fixed upper end and constant 1.6 N / m has a 400 g object suspended a 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 (2t) Xg = 0,15 m x% =1,2 m/S (b) Determine the position of the object at any time t. X (+) = L0,1S cos ( 2+)+0,6 sin (2t) (c) Indicate whether this system enters mechanical resonance. Justify,
A vertical spring with a fixed upper end and constant 1.6 N / m has a 400 g object suspended a 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 (2t) Xg = 0,15 m x% =1,2 m/S (b) Determine the position of the object at any time t. X (+) = L0,1S cos ( 2+)+0,6 sin (2t) (c) Indicate whether this system enters mechanical resonance. Justify,
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter16: Oscillations
Section: Chapter Questions
Problem 74PQ: The total energy of a simple harmonic oscillator with amplitude 3.00 cm is 0.500 J. a. What is the...
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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 (2t) X= 0,15 m x%=1,2m/s
(b) Determine the position of the object at any time t.
X (t) = L 0,15 cos (2+)+0,6 sin(2t)
(c) Indicate whether this system enters mechanical resonance. Justify,
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