I want to confirm a solution that I have for this problem. Please show all steps

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I want to confirm a solution that I have for this problem. Please show all steps. If you have already anwsered this problem for me please do not anwser again at this time. Thank you.

Driven Moiton / Forced Motion with damping differential equations



A mass streches a spring 2.45m whose spring constant is 8N/m. The mass is intially released from the equilibrium position with a downward velocity of 1/25 m/s, and the subsequent motion takes motion takes place in a medium that offers a damping force that is numerically equal to 8 times the instantaneously velocity. Find the equation of the motion if the mass is driven by an external force equal to f(t) = 2e-tcos2

Identify the following for the associated homgenous DE

auxiliary equation:__________ ; Find both roots of the auxiliary equation________________

Find both solutions of the auxiliary equation: Xc1(t)=____________& Xc2(t)=_______________

Give the complementary function to the DE above (use C1 and C2 for the undetermined coefficients):

Xc(t)=________________________________________________________________________

Identify the following when using the annihilator approach: F(t)=__________________________

Which differential operator is used to annihilate F(t)?

Give the aprticular solution to the nonhomgenous DE (use A and B for the undetermined coefficients):

Xp(t)=__________________________________________________________________________

To find the undetermined coefficents A and B of the particular solution you will also need:

X/p(t)=___________________________________________________________________________

X//p(t)=___________________________________________________________________________

Write the general solution to the equation of motion, x(t)=xc(t)+xp(p), as a function of time,t.

to find the undetermined coefficients C1 and C2 with the intial conditions given , you will aslo need:

X/(t)=____________________________________________________________________________________

The Equation of Motion is x(t) = ________________________________________________________________

Explanation / Answer

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