For the following forcing inputs, assume u(0) = 0 and u(0)=0. Use Duhamel's Integral to find the response of a mass-spring system (undamped system) to the following in (forces): Solve using the principle of superposition. Only do the appropriate sketching for this proble A plt) Po Po cos(nt/2t)

For the following forcing inputs, assume u(0) = 0 and u(0)=0. Use Duhamel's Integral to find the response of a mass-spring system (undamped system) to the following in (forces): Solve using the principle of superposition. Only do the appropriate sketching for this proble A plt) Po Po cos(nt/2t)

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter15: Oscillations

Section: Chapter Questions

Problem 21P: Prove that using x(t)=Asin(t+) will produce the same results for the period for the oscillations of...

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Equation of Waves

Wave is an oscillation or disturbance traveling in a medium. It performs the transportation of energy but does not carry any matter. This motion of waves will transport fuel in a medium without permanent transfer of mass (particle).

Question

Please do not copy already posted answers, they are incorrect. Attached is hint functions for problem solution process.

For the following forcing inputs, assume u(0) = 0 and u(0)= 0. Use Duhamel's
Integral to find the response of a mass-spring system (undamped system) to the following inputs
(forces):
Solve using the principle of superposition. Only do the appropriate sketching for this problem.
A P(t)
Po
Po cos(mt/2td)

u(t) is obtained using Duhammel's integral
P(t)= P cos at where @
π
21
For 0≤t<t
|u(t)=P(t)h(t-1)dt
= (P. cos @T) h(t-1)dt
= [ (Po cos@7) sin@₁₂(t-1)
mon
Fort2t
|u(t)=P(t)h(t-1)dt
P1
t1
(0
(cos@t-cos@t) where r=-
-P1
11
-P2
P2
12

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