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A 1-kilogram mass is attached to a spring whose constant is 27 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 12 times the instantaneous velocity. Determine the equations of motion if the following is true.(a) the mass is initially released from rest from a point 1 meter below the equilibrium positionx(t)=_________________________________________m(b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 11 m/sx(t)=___________________________________________m

Question

A 1-kilogram mass is attached to a spring whose constant is 27 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 12 times the instantaneous velocity. Determine the equations of motion if the following is true.

(a) the mass is initially released from rest from a point 1 meter below the equilibrium position

x(t)=_________________________________________m

(b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 11 m/s

x(t)=___________________________________________m

check_circleAnswer
Step 1

Given,

m 1 kg
k 27 N/m
F 12 12x
c 12
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m 1 kg k 27 N/m F 12 12x c 12

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Step 2

As we know equation used for damping

тх + сх + h 3 0
х +12х + 27х %3D0
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тх + сх + h 3 0 х +12х + 27х %3D0

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Step 3

To solve the give...

(m+9)(m+3) 0
m -9,-3
x() - Се " +C,е
-9t
-3г
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(m+9)(m+3) 0 m -9,-3 x() - Се " +C,е -9t -3г

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