Question

_{4 HW_2nd ODE Application Part A) Mass spring damper system as represented in the figure. If the block has a mass of 0.25 (kg) started vibrated freely from rest at the equilibrium position, the spring is a massless with a stiffness of 4 (N/m) and the damping coefficient C (Ns/m) such that c is less than 4 Ns/m. Find all possible equations of motion for the block. k 772 TH Part B) If a two DC motors applied an external force and so, Find the equations of motion for the block released from rest under these excited forces.}

Answer 1

kx e M +20 Solutions A H că - K = 4 Nm Ostiffness) C = 4 Nym ( dumping offiant) m=0.25kg (mass Then the equation of motion mx + (x + KX=0 put the valu 0.25% tux tux=0 ťë tux tux=0 ☆ + 16 + 16x=0 (m) Roots of equation - m=-16 I 516² 4X16* 2 m =-16 + √256-64 2 m= 16 I 192 2.

(-16-2192)+ (-16 +5192)+ pe(a) = Ge 2 + G * applied a fara on the system, at(a) cas KXE m 2x mic+ cx + KX=flt) Since the equation is non homogenous, its gumal solution (0/1)) is given by - X(t) Hylt) + Belt) D4U) - homogruous solution Aplt) Particular solution. where, X(+) = Ge t (-164 JELSE (-16-2192) + &(1) - When function is given then find the value directly when D is Dt16D+16 differential operator 1 38(t) = t(A)