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A 10-kg mass attached to a spring with stiffness 250 N/m, with negligible resistance. Initially, the string is contracted by 15 cm relative to its natural length and the mass is moving outward (i.e. towards the equilibrium position) at 1 m/sec. (a) Sketch a diagram, indicate the variables and units and state differential equation and the intial conditions for x(t), the position of the mass as a function of time. (b) Determine an explicit formula for x(t) and the amplitude of the resulting oscillations. Include the appropriate units. (c) Use the formula in part b to find the earliest positive time when the direction of mo- tion reverses from outward to inward (equivalently, the string is stretched as much as possible).

A 10-kg mass attached to a spring with stiffness 250 N/m, with negligible resistance. Initially, the string is contracted by 15 cm relative to its natural length and the mass is moving outward (i.e. towards the equilibrium position) at 1 m/sec. (a) Sketch a diagram, indicate the variables and units and state differential equation and the intial conditions for x(t), the position of the mass as a function of time. (b) Determine an explicit formula for x(t) and the amplitude of the resulting oscillations. Include the appropriate units. (c) Use the formula in part b to find the earliest positive time when the direction of mo- tion reverses from outward to inward (equivalently, the string is stretched as much as possible).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A 10-kg mass attached to a spring with stiffness 250 N/m, with negligible resistance. Initially, the string is contracted by 15 cm relative to its natural length and the mass is moving outward (i.e. towards the equilibrium position) at 1 m/sec. (a) Sketch a diagram, indicate the variables and units and state differential equation and the intial conditions for x(t), the position of the mass as a function of time. (b) Determine an explicit formula for x(t) and the amplitude of the resulting oscillations. Include the appropriate units. (c) Use the formula in part b to find the earliest positive time when the direction of mo- tion reverses from outward to inward (equivalently, the string is stretched as much as possible).
Transcribed Image Text:A 10-kg mass attached to a spring with stiffness 250 N/m, with negligible resistance. Initially, the string is contracted by 15 cm relative to its natural length and the mass is moving outward (i.e. towards the equilibrium position) at 1 m/sec. (a) Sketch a diagram, indicate the variables and units and state differential equation and the intial conditions for x(t), the position of the mass as a function of time. (b) Determine an explicit formula for x(t) and the amplitude of the resulting oscillations. Include the appropriate units. (c) Use the formula in part b to find the earliest positive time when the direction of mo- tion reverses from outward to inward (equivalently, the string is stretched as much as possible).
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