A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium positon with an upward velocity of 12m/s. -2 -2t 5 8t

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid
that imparts a damping force numerically equal to 10 times the instantaneous velocity. Determine the equation of
motion if the mass is initially released from a point 1 meter below the equilibrium positon with an upward velocity of
12m/s.
-2
u(t)=
5
.-2t
-8t
e + e
3
3
5
u(t)=
= 1/²/3e-2t +
-8t
е
e
3
O
5
|u(t)==-e-2t₁ -8t
3
Ⓒu(t)=²8-2 +²²
=
шыш
Transcribed Image Text:A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium positon with an upward velocity of 12m/s. -2 u(t)= 5 .-2t -8t e + e 3 3 5 u(t)= = 1/²/3e-2t + -8t е e 3 O 5 |u(t)==-e-2t₁ -8t 3 Ⓒu(t)=²8-2 +²² = шыш
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