What is occurring in the umbra?
1 answer:
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Answer:
t = 025 s
Explanation:
We know
weight, W = 4 pounds
spring constant, k = 2 lb/ft
Positive damping, β = 1
Therefore mass, m = W / g
m = 4 / 32
= 1 / 8 slug
From Newtons 2nd law
where x(t) is the displacement from the mean or equilibrium position. The equation can be written as
Substituting the values, the DE becomes
Now the equation is
and on solving the roots are
=
= -4
Therefore the general solution is
Now for initial condition x(0) = -1 ft
x'(0)= 8 ft/s
Now we can find the equation of motion becomes,
Therefore, the mass passes through the equilibrium when
x(t) = 0
= 0
-1+4t = 0
t =
= 0.25 s