The mass, m = 3… kg
The spring constant,
k = 151 N/m
The damping constant of
the oil, b = 10.3 kg/s
a)
The displacment equation for
the damped oscillator is
x(t)
=
xme(-b/2m)t
Given that,
x/xm = 0.01 ( that is 1% of the original
)
So the above equation
changes to,
e(-b/2m)t
= 0.017
Apply the natural
logerethms on both sides, we get
[-b/2m]t
= ln(0.017)
Therefore, the required
time is
t
= ln(0.017)/[-b/2m]
=
-2mln(0.017)/b
=
-(2)(3.33 kg)ln(0.017)/(10.3 kg/s)
=
2.63 s
b)
The time t =1.30
s
Then,
x/xm = 100% - 98.3%
= 1.7%
= 0.017
From equation (1), the
damping constant is
b
= -(2m/t) ln (x
/xm)
= -(2)(3.33 kg)ln(0.017)/(1.3 s)
= 20.9 kg/s
=
21 kg/s
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