A mass m of a spring with constant k satisfies the equation mu" + ku = 0, where u (t) is the displacement at time t of the mass from the equilibrium position. a) Show that this equation can be converted into the system -k/m b) Find the solution of the initial value problem if the position of the spring at time O is 2 cm below the equilibrium position and its velocity is 0 cm / s. k) Graph the velocity and position on a single Cartesian plane.
A mass m of a spring with constant k satisfies the equation mu" + ku = 0, where u (t) is the displacement at time t of the mass from the equilibrium position. a) Show that this equation can be converted into the system -k/m b) Find the solution of the initial value problem if the position of the spring at time O is 2 cm below the equilibrium position and its velocity is 0 cm / s. k) Graph the velocity and position on a single Cartesian plane.
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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Can you help me with this problem please? Especially with the part b and c. I attach the image of the problem
Transcribed Image Text:A mass m of a spring with constant k satisfies the equation
mu" + ku = 0,
where u (t) is the displacement at time t of the mass from the equilibrium position.
a) Show that this equation can be converted into the system
-k/m
b) Find the solution of the initial value problem if the position of the spring at time
O is 2 cm below the equilibrium position and its velocity is 0 cm / s.
k) Graph the velocity and position on a single Cartesian plane.
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