Write the given second order equation as its equivalent system of first order equations. u" + 4.5u' – 7.5u = -7 sin(3t), u(1) = -7.5, u'(1) = -6 Use v to represent the "velocity function", i.e. v = Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) = u'(t).

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ISBN:9781337282291
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Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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Write the given second order equation as its equivalent system of first order equations.
u" + 4.5u' – 7.5u = -7 sin(3t),
u(1) = -7.5,
u'(1) = -6
Use v to represent the "velocity function", i.e. v = u'(t).
Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.)
u' =
%3D
Now write the system using matrices:
u
d
+
dt
V
V
and the initial value for the vector valued function is:
u(1)
v(1)
Transcribed Image Text:Write the given second order equation as its equivalent system of first order equations. u" + 4.5u' – 7.5u = -7 sin(3t), u(1) = -7.5, u'(1) = -6 Use v to represent the "velocity function", i.e. v = u'(t). Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) u' = %3D Now write the system using matrices: u d + dt V V and the initial value for the vector valued function is: u(1) v(1)
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