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7. Find the general solution r(t) to d²r/dt²=w²r with w real and constant.

7. Find the general solution r(t) to d²r/dt²=w²r with w real and constant.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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7. Find the general solution r(t) to d²r/dt²= w²r with w real and constant. 8. Investigate r(t) if md²r/dt² -k(r-lo) for constant m and arbitrary initial conditions r(0) = ro and v(0) = vo, where v dr/dt, r = rf, with k, lo constant (modeling a spring of stiffness k and rest length lo). Can you find conserved quantities? Can you define a potential V(r) for this problem? What type of motion do you expect? Are there special initial conditions?
Transcribed Image Text:7. Find the general solution r(t) to d²r/dt²= w²r with w real and constant. 8. Investigate r(t) if md²r/dt² -k(r-lo) for constant m and arbitrary initial conditions r(0) = ro and v(0) = vo, where v dr/dt, r = rf, with k, lo constant (modeling a spring of stiffness k and rest length lo). Can you find conserved quantities? Can you define a potential V(r) for this problem? What type of motion do you expect? Are there special initial conditions?
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