Hoote Law and Differential Equations Questions

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I will send my answer. I want you to review and fix the correct.here is a question :
A 10-lb weight is attached to a spring suspended from the ceiling. When the weight comes to rest, the spring is stretched by 1.5 inches.The damping constant for the system is 5*sqrt(2) lbs/(ft/sec). The weight is pulled down 3 inches from the equilibrium position and released.
a) determine the motion of the weight.b) Determine the damped amplitude, damped natural frequency, and damped period of the subsequent motion.

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natural frequency, and damped period of the
Subsequent motion.
ma
2
3100
– 10 lb
32 ft/sec
–
5
16
Ib-sec²
ft
is slug
a)
d=o
K = w
AL
lolb
80 lb ь
24 = 80
1.5 ft
ft
X 11
mx X
+ Kx = 0
5
16
aloo }
x
+ 80x = 0
& Co)
3 ft = 4 ft x'(o)=0 ft/sec
5
16
x”+80x=0
x 256x=0
D² +256 = 0 D = = 16 i
x (t)=C, Cos(16t) + C₂ sin (16t)
x'(t) = -16c, sin (16t) + 16 Cz Cos (16t)
x(0) = / 4 = cito C =
x'(o)=o=0+16c2
> C2 = 0
= 44 Cos (16t)
x
X(t)

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Tags:
differential equation

subsequent motion

damping constant

modeling of system

Hoote Law

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