Respuesta :
Answer:
The initial value problem is given by
16 u'' + 400 u' + 3203 u = 0 , u (o) = 0 & u' (0) = 0.05 [tex]\frac{m}{s}[/tex]
Explanation:
Given data
m = 16 kg
L = 4.9 cm = 0.049 m
Viscous force F = 4 N
Sped of the mass u' (t) = 1 [tex]\frac{cm}{s}[/tex] = 0.01 [tex]\frac{m}{s}[/tex]
u (o) = 0
u' (0) = 0.05 [tex]\frac{m}{s}[/tex]
We know that [tex]W = k L[/tex]
K = [tex]\frac{16 (9.81)}{0.049}[/tex]
k = 3203 [tex]\frac{N}{m}[/tex]
This is the stiffness of the spring.
We know that viscous force F = c u' (t)
Where c = damping constant
[tex]c = \frac{4}{0.01}[/tex]
C = 400 N
Therefore the initial value problem is given by
m u'' + c u' + k u = 0
16 u'' + 400 u' + 3203 u = 0 , u (o) = 0 & u' (0) = 0.05 [tex]\frac{m}{s}[/tex]
