A mass-spring system with a hardening spring, linear viscous damping, and a periodic external force can...

 

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A mass-spring system with a hardening spring, linear viscous damping, and a periodic external force can be represented by the Duffing's equation mỹ +cy +ky +ka’y = A cos at Take a Lyapunov function .2. 3 3 1 1 (x ) =* x +x where x, =y and x, =y. 1 T. 4 %3D 2 a) Determine the functions a, (| x |I) EK and a,(| x ||) eK satisfying the inequality a, (|| x |) <V <a,(|x ||) b) Determine the quantity u> 0 and a continuous positive definite function W (x ) satisfying the inequality V <-W (x ), ▼||x ||> µ - A mass-spring system with a hardening spring, linear viscous damping, and a periodic external force can be represented by the Duffing's equation mỹ +cy +ky +ka’y = A cos at Take a Lyapunov function .2. 3 3 1 1 (x ) =* x +x where x, =y and x, =y. 1 T. 4 %3D 2 a) Determine the functions a, (| x |I) EK and a,(| x ||) eK satisfying the inequality a, (|| x |) <V <a,(|x ||) b) Determine the quantity u> 0 and a continuous positive definite function W (x ) satisfying the inequality V <-W (x ), ▼||x ||> µ -

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First of all we have to understand that the equation is ... View the full answer