Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. Knight P11.74 Given the equation of position versus time, x(t) = Ae-t cos(wt + o) Show that the time derivatives of this equation are: dx dt d²x dt2 - Aße-t cos(wt + o) - Awe-t sin(wt + o) =(A3² - Aw²) e-t cos(wt + 0) +2Aßwe-t sin(wt + o)

1. Knight P11.74 Given the equation of position versus time, x(t) = Ae-t cos(wt + o) Show that the time derivatives of this equation are: dx dt d²x dt2 - Aße-t cos(wt + o) - Awe-t sin(wt + o) =(A3² - Aw²) e-t cos(wt + 0) +2Aßwe-t sin(wt + o)

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
See similar textbooks
icon
Related questions
Question
Help with the following question
Questions In the following three exercises you will solve the Newton's second law equation for a horizontal oscillating spring with spring constant, k, and linear drag coefficient, b. 1. Knight P11.74 Given the equation of position versus time, 2 x(t) = Ae-t cos(wt + o) Show that the time derivatives of this equation are: dx Aße-t cos(wt + o) dt == d²x dt² - Awe-Bt =(A3² - Aw²) e-Bt cos(wt + po) +2Aßwe-t sin(wt + o) t sin(wt + o) Substitute your answer from Q1 into the
Transcribed Image Text:Questions In the following three exercises you will solve the Newton's second law equation for a horizontal oscillating spring with spring constant, k, and linear drag coefficient, b. 1. Knight P11.74 Given the equation of position versus time, 2 x(t) = Ae-t cos(wt + o) Show that the time derivatives of this equation are: dx Aße-t cos(wt + o) dt == d²x dt² - Awe-Bt =(A3² - Aw²) e-Bt cos(wt + po) +2Aßwe-t sin(wt + o) t sin(wt + o) Substitute your answer from Q1 into the
Useful information Product rule Trig derivatives d(uv) = du v + u dv d du d du cos au = -a sin au sin au= a cos au Derivative of natural log base d - eau = aeau du Sine plus cosine equation: if the sum of sines and co- is zero for all angles, then the coefficients of the sine and cosines are themselves identically zero 0= P cos u + Q sin u P = 0 Q=0
Transcribed Image Text:Useful information Product rule Trig derivatives d(uv) = du v + u dv d du d du cos au = -a sin au sin au= a cos au Derivative of natural log base d - eau = aeau du Sine plus cosine equation: if the sum of sines and co- is zero for all angles, then the coefficients of the sine and cosines are themselves identically zero 0= P cos u + Q sin u P = 0 Q=0
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
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,
SEE MORE TEXTBOOKS