in regards to convolution intergal can you explain process

Find the displacement response of a SDOF system with $m = 20 kg, c = 30 N . s / m, k = 5, 000 N / m$ , $x_{0} = 0.02 m, \overset{x}{˙}_{0} = 0.5 m / s$ subjected to an external force $F (t) = F_{0} sin ω t$ with $F_{0} = 120 N$ and $ω = 15 rad / s$ using the regular differential equations solution as well as the convolution integral methods. Plot, compare and interpret the results.

Question

in regards to convolution intergal can you explain process

Find the displacement response of a SDOF system with

m = 20 kg, c = 30 N . s / m, k = 5, 000 N / m

,

x_{0} = 0.02 m, \overset{x}{˙}_{0} = 0.5 m / s

subjected to an external force

F (t) = F_{0} sin ω t

with

F_{0} = 120 N

and

ω = 15 rad / s

using the regular differential equations solution as well as the convolution integral methods. Plot, compare and interpret the results.

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