Consider the following various differential equations that describe the mass- spring systems. A. y''+y=0 B. y''+9y=3sin(9t)...

Consider the following various differential equations that describe the mass-

spring systems.

A. y''+y=0

B. y''+9y=3sin(9t)

C. y''+y=5cos(t)

D. y''+400y=sin(19t)

E. y''+4y'+5y=0

F. y''+6y'+9y=0

(I) Which system is undergoing resonance?

(II) Which system is critically damped?

(III) Which system gives damped oscillation as the solution?

(IV) Which system describes undamped free oscillation?

(V) What is the frequency and period of the case (A)?

(VI) What is the quasi-frequency and quasi-period of the case (E)?

Expert Solution

Colby Messinger answered 1 month ago

y″+9y′=162sin(9t)+324cos(9t) y(0)=7 y'(0)=7

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