For the following forcing inputs, assume u(0) =0 and iù(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. Po 다 ta
For the following forcing inputs, assume u(0) =0 and iù(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. Po 다 ta
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Please do not copy already posted work, it is incorrect. Attached is hint to solve problem.
Transcribed Image Text:u(t) is obtained using Duhammel's integral
P₁
P(1) - Pet
For 0<t St
u(t)=P(r)h(t-r)dr
"
P1
Prh(t-1)dt
For 1>
k of.
where k = ma
u(t)=P(t)h(t-1)dt
-² (cc
k
PO
sin a, (1-1) dr
mas
-(@t-sinat) (see Eq. 7.31 in note)
td
sin , (1-1) dr
ma
cosa, (t−1₂) + —_—_—_ (sin c, (t−†₂)-sinot)
+
td
-PO
Transcribed Image Text: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.
4 pit)
Po
E
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