Question

Shies Paragraph HW 2-ODE Application Part Al Mass spring damper system as represented in the figure. If the block has a mass of 0.25 g started vibrated freely from rest at the equilibrium position, the spring is a massless with a stiffness of (N/m) and the damping coefficient ciNs/m such that is less than 4 Na/m. Find all possible equations of motion (t) for the block Part If two DC motors applied an external force (t) = n(t) and (t) tt) = f(t) + f(t) Find the equations of motion for the block released from rest under these excited forces

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Answer 1

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Above image is the procedure to solve whenthere is sine or cosine term.

dh xuss eof sine kleal 0,25x-1 + 40+4 Up = sine 3.75 +40 gp= sine (3.75-4D) (3.75 +4D) (3,75-4D) - 3.75 sinx - 4D(sine) B (3,757² 4²-02 but D²=-| 3,75 sinx - 4D sinx = 3.752+16 1 lyfr 30.0625[3.75 3,75 sinx - 4lose Total solution, complimentary tYPI solutions have t For solving the above ODEs, you some baste algorithms for to study cach cases

B = 4.14 m/s of for the please give thumbs up hard work. If you are not satisfied with the answer please comment before giving la dislike.