9) A force of 84 N stretches a spring 3 m. A mass weighing 39.2 N is attached to the end of this spring and released from 1 m above equilibrium with an initial downward velocity of 2 m/s. The subsequent motion takes place in a medium that offers a damping force numerically equal to 16 times the instantaneous velocity of the mass. Write the initial value problem that the position function x(t) of the mass satisfies. Use the convention x(t) > 0 + the mass is below equilibrium. Acceleration of gravity is g = 9.8 m/s² a) 39.2x" + 16x' + 28x = 0 , x(0) = -1, x'(0) = 2 %3D b) 39. 2x" + 16x' + 28x = 0, x(0) = -1, x'(0) = -2 c) 4x" + 16x' + 28x = 0 , x(0) = 1, x'(0) = -2 d) x" + 4x' + 7x = 0 , x(0) = -1, x'(0) = 2 %3D
9) A force of 84 N stretches a spring 3 m. A mass weighing 39.2 N is attached to the end of this spring and released from 1 m above equilibrium with an initial downward velocity of 2 m/s. The subsequent motion takes place in a medium that offers a damping force numerically equal to 16 times the instantaneous velocity of the mass. Write the initial value problem that the position function x(t) of the mass satisfies. Use the convention x(t) > 0 + the mass is below equilibrium. Acceleration of gravity is g = 9.8 m/s² a) 39.2x" + 16x' + 28x = 0 , x(0) = -1, x'(0) = 2 %3D b) 39. 2x" + 16x' + 28x = 0, x(0) = -1, x'(0) = -2 c) 4x" + 16x' + 28x = 0 , x(0) = 1, x'(0) = -2 d) x" + 4x' + 7x = 0 , x(0) = -1, x'(0) = 2 %3D
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Transcribed Image Text:9) A force of 84 N stretches a spring 3 m. A mass weighing 39.2 N is attached to the end of this spring and
released from 1 m above equilibrium with an initial downward velocity of 2 m/s. The subsequent motion
takes place in a medium that offers a damping force numerically equal to 16 times the instantaneous velocity
of the mass. Write the initial value problem that the position function x(t) of the mass satisfies.
Use the convention x(t) > 0 + the mass is below equilibrium. Acceleration of gravity is g = 9.8 m/s²
a) 39.2x" + 16x' + 28x = 0 , x(0) = –1, x'(0) = 2
b) 39. 2x" + 16x' + 28x = 0, x(0) = -1, x'(0) = -2
с) 4x" + 16х' + 28х — 0,
x(0) 3 1, х'(0) - —2
I|
d) x" + 4x' + 7x = 0 , x(0) = -1, x'(0) = 2
e) x" + 4x' + 7x = 9.8 , x(0) = -1, x'(0) = 2
%3|
%3D
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