22. A mass weighing 4 pounds stretches a spring 4 inches. (a) Formulate an initial-value problem that corresponds to the motion of this un- damped mass-spring system if the mass is extended 1 foot from its rest position and released (with no initial velocity). (b) Using the result of Exercise 20, find the solution of this initial-value problem.
22. A mass weighing 4 pounds stretches a spring 4 inches. (a) Formulate an initial-value problem that corresponds to the motion of this un- damped mass-spring system if the mass is extended 1 foot from its rest position and released (with no initial velocity). (b) Using the result of Exercise 20, find the solution of this initial-value problem.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Help asap!! #22 only !
![20. Consider the equation
+
dt² m
for the motion of a simple harmonic oscillator.
0
(a) Consider the function y(t) = cos ßt. Under what conditions on ß is y(t) a
solution?
(b) What initial condition (t = 0) in the yv-plane corresponds to this solution?
(c) In terms of k and m, what is the period of this solution?
(d) Sketch the solution curve (in the yv-plane) associated to this solution. [Hint:
Consider the quantity y² + (v/B)².]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F464fe16a-00d5-4182-8379-61bd4b8bbe02%2Fbdb2e5cf-a9b0-470a-95c1-3ea24c49ea47%2Fm9kwcdp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:20. Consider the equation
+
dt² m
for the motion of a simple harmonic oscillator.
0
(a) Consider the function y(t) = cos ßt. Under what conditions on ß is y(t) a
solution?
(b) What initial condition (t = 0) in the yv-plane corresponds to this solution?
(c) In terms of k and m, what is the period of this solution?
(d) Sketch the solution curve (in the yv-plane) associated to this solution. [Hint:
Consider the quantity y² + (v/B)².]
Transcribed Image Text:2.1 Modeling via Systems 165
21. A mass weighing 12 pounds stretches a spring 3 inches. What is the spring constant
for this spring?
22. A mass weighing 4 pounds stretches a spring 4 inches.
(a) Formulate an initial-value problem that corresponds to the motion of this un-
damped mass-spring system if the mass is extended 1 foot from its rest position
and released (with no initial velocity).
(b) Using the result of Exercise 20, find the solution of this initial-value problem.
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