Asked by Chad
A system is represented by the equation:
2x”+128x = f(t)
Obtain the free response of the system in the form
a) x = A sin wn (t ) + B cos wn (t)
b) x= A sin wn (t) + ϕ
The initial conditions are x(0) = 0.05m and x’ = 0.3m/s.
2x”+128x = f(t)
Obtain the free response of the system in the form
a) x = A sin wn (t ) + B cos wn (t)
b) x= A sin wn (t) + ϕ
The initial conditions are x(0) = 0.05m and x’ = 0.3m/s.
Answers
Answered by
Redley
a.
√(128/2) = 8.
x=(-0.3/8)sin8t+0.05cos8t
x=-0.0375sin8t+0.05cos8t
b.
A=+√( (0.05)^2 + ((-0.3)^2/(8)^2) ) = 0.062
sinϕ= (0.05/0.062) =0.806
cosϕ= (-0.3/0.062 *8) =-0.605
ϕtan= tan^-1 (0.806/-0.605) = tan^-1 (-1.333)=-0.927
-0.0927+π=2.217 rad
x= 0.062sin ( 8t + 2.214)m
√(128/2) = 8.
x=(-0.3/8)sin8t+0.05cos8t
x=-0.0375sin8t+0.05cos8t
b.
A=+√( (0.05)^2 + ((-0.3)^2/(8)^2) ) = 0.062
sinϕ= (0.05/0.062) =0.806
cosϕ= (-0.3/0.062 *8) =-0.605
ϕtan= tan^-1 (0.806/-0.605) = tan^-1 (-1.333)=-0.927
-0.0927+π=2.217 rad
x= 0.062sin ( 8t + 2.214)m
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