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State the initial value problem describing the mass's motion upon starting from its release, Solution: Displacement y from equilibrium solves the equation given in the lecture y" the initial values given in the problem are y(0) = 0 and y'(0) = 0.01. Solve the initial value problem formulated in (b). Solution: The root oquation has solutions I k ===y=-500y, m 500 So the general coltuion is

State the initial value problem describing the mass's motion upon starting from its release, Solution: Displacement y from equilibrium solves the equation given in the lecture y" the initial values given in the problem are y(0) = 0 and y'(0) = 0.01. Solve the initial value problem formulated in (b). Solution: The root oquation has solutions I k ===y=-500y, m 500 So the general coltuion is

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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Problem 2: A 100 gram mass, when attached to a spring hanging vertically, stretches the spring 2cm. The mass is then released from the equilibrium position with an initial velocity 1cm/s. Assume that there is no dumping. (a) Determine the spring constant k, Solution: Equating the gravitational force and spring force I get 50Nm-¹. k = mg Ax 10 × 0.1 0.02 (b) State the initial value problem describing the mass's motion upon starting from its release, Solution: Displacement y from equilibrium solves the equation given in the lecture y" the initial values given in the problem are y(0) = 0 and y'(0) = 0.01. (c) Solve the initial value problem formulated in (b). Solution: The root equation has solutions > = k -y = = -500y, m +√500i. So the general soltuion is y(t) = C₁ sin(√500t) + C₂ cos(√500t). Using the initial values I get C₂ = 0 and √500C₁ = 0.01 so 0.01 y(t) sin(√500). √500
Transcribed Image Text:Problem 2: A 100 gram mass, when attached to a spring hanging vertically, stretches the spring 2cm. The mass is then released from the equilibrium position with an initial velocity 1cm/s. Assume that there is no dumping. (a) Determine the spring constant k, Solution: Equating the gravitational force and spring force I get 50Nm-¹. k = mg Ax 10 × 0.1 0.02 (b) State the initial value problem describing the mass's motion upon starting from its release, Solution: Displacement y from equilibrium solves the equation given in the lecture y" the initial values given in the problem are y(0) = 0 and y'(0) = 0.01. (c) Solve the initial value problem formulated in (b). Solution: The root equation has solutions > = k -y = = -500y, m +√500i. So the general soltuion is y(t) = C₁ sin(√500t) + C₂ cos(√500t). Using the initial values I get C₂ = 0 and √500C₁ = 0.01 so 0.01 y(t) sin(√500). √500
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