The cart in the figure below weighs 64 pounds and is attached to the wall by a spring with spring constant k = 32 lb/ft. The cart is pulled 3 inches in the direction away from the wall and released with no initial velocity. Simultaneously a periodic external force Fe = f (t) = 16 cos 4t is applied to the cart. Assuming that there is no air resistance, find the position x = x(t) of the cart at time t. Note particularly that |x(t)| has arbitrarily large values as t → o, a phenomenon known as pure resonance and caused by the fact that the forcing function has the same period as the free vibrations of the unforced system. M о

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
The cart in the figure below weighs 64 pounds and is attached to the wall by a spring with
spring constant k = 32 lb/ft. The cart is pulled 3 inches in the direction away from the wall
and released with no initial velocity. Simultaneously a periodic external force Fe = f (t) =
16 cos 4t is applied to the cart. Assuming that there is no air resistance, find the position x =
x(t) of the cart at time t. Note particularly that |x(t)| has arbitrarily large values as t → o, a
phenomenon known as pure resonance and caused by the fact that the forcing function has the
same period as the free vibrations of the unforced system.
M
о
Transcribed Image Text:The cart in the figure below weighs 64 pounds and is attached to the wall by a spring with spring constant k = 32 lb/ft. The cart is pulled 3 inches in the direction away from the wall and released with no initial velocity. Simultaneously a periodic external force Fe = f (t) = 16 cos 4t is applied to the cart. Assuming that there is no air resistance, find the position x = x(t) of the cart at time t. Note particularly that |x(t)| has arbitrarily large values as t → o, a phenomenon known as pure resonance and caused by the fact that the forcing function has the same period as the free vibrations of the unforced system. M о
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,