Solve the problem of resonance damped vibration of a spring .If the governing D.E is given by (m frac{d^2 y}{dt^2} + c frac{dy}{dt} + ky=0; ) c0 with initial conditions as y(0)=y0 and y (0)=y1 and assume c/m=2 , k/m= 2 and (v = sqrt{ ^2- ^2} ).

Question

Solve the problem of resonance damped vibration of a spring .If the governing D.E is given by  (m  frac{d^2 y}{dt^2} + c  frac{dy}{dt} + ky=0; ) c>0 with initial conditions as y(0)=y0 and y (0)=y1 and assume c/m=2 , k/m= 2 and  (v =  sqrt{ ^2- ^2} ).

TuteeHUB · Accepted Answer

y = e^(- t) ( ( left( frac{y_1+ y_0}{v} right) ) cos u2061vt + y₀ sin u2061vt)

TuteeHUB · Answer

y = e- t (y0 cos u2061vt + y1 sin u2061vt)

TuteeHUB · Answer

y = e^(-  t) (y0 cos u2061vt+  (  left(  frac{y_1+  y_0}{v}  right)  ) sin u2061vt)

TuteeHUB · Answer

y = e^(-  t) (  (  left(  frac{y_1+  y_0}{v}  right)  ) cos u2061vt + y0 sin u2061vt)

TuteeHUB · Answer

y = e- t (y0 cos u2061vt+ y1 sin u2061vt)

1.	Solve the problem of resonance damped vibration of a spring .If the governing D.E is given by (m frac{d^2 y}{dt^2} + c frac{dy}{dt} + ky=0; ) c>0 with initial conditions as y(0)=y₀ and y (0)=y₁ and assume c/m=2 , k/m= ² and (v = sqrt{ ^2- ^2} ).
A.	y = e<sup>- t</sup> (y<sub>0</sub> cos u2061vt + y<sub>1</sub> sin u2061vt)
B.	y = e^(- t) (y<sub>0</sub> cos u2061vt+ ( left( frac{y_1+ y_0}{v} right) ) sin u2061vt)
C.	y = e^(- t) ( ( left( frac{y_1+ y_0}{v} right) ) cos u2061vt + y<sub>0</sub> sin u2061vt)
D.	y = e<sup>- t</sup> (y<sub>0</sub> cos u2061vt+ y<sub>1</sub> sin u2061vt)
Answer» C. y = e^(- t) ( ( left( frac{y_1+ y_0}{v} right) ) cos u2061vt + y<sub>0</sub> sin u2061vt)

Solve the problem of resonance damped vibration of a spring .If the governing D.E is given by (m frac{d^2 y}{dt^2} + c frac{dy}{dt} + ky=0; ) c>0 with initial conditions as y(0)=y₀ and y (0)=y₁ and assume c/m=2 , k/m= ² and (v = sqrt{ ^2- ^2} ).

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