x"+4x=0, x(0)=1, x'(0)=-2
please show me how to find the amplitude, phaseangle, and period!
i got as far as utilizing the characteristic equation...
x^2+4 =0
x = +/- 2i
x(t) = Acos(2t)+Bisin(2t)
then using the initial conditions..
x(0)=1 => cos(2t)+Bisin(2t)
take the derivative...
x'(t)=-2sin(2t)+2Bicos(2t)
-2 = x'(0) => 0 +2Bi
divide both sides by 2i
B= -1/i
x(t) = cos(2t)-sin(2t)
i figured the amplitude would be 1? but it's not... and i think the period 2pi? no clue as to what a phaseangle is =T help please! thanks ^_^
please show me how to find the amplitude, phaseangle, and period!
i got as far as utilizing the characteristic equation...
x^2+4 =0
x = +/- 2i
x(t) = Acos(2t)+Bisin(2t)
then using the initial conditions..
x(0)=1 => cos(2t)+Bisin(2t)
take the derivative...
x'(t)=-2sin(2t)+2Bicos(2t)
-2 = x'(0) => 0 +2Bi
divide both sides by 2i
B= -1/i
x(t) = cos(2t)-sin(2t)
i figured the amplitude would be 1? but it's not... and i think the period 2pi? no clue as to what a phaseangle is =T help please! thanks ^_^
-
x(t)
= cos(2t) - sin(2t)
= sqrt(2) [ cos(2t) cos(pi/4) - sin(2t) sin(pi/4) ]
= sqrt(2) cos(2t+pi/4)
The rest should be easy for you.
= cos(2t) - sin(2t)
= sqrt(2) [ cos(2t) cos(pi/4) - sin(2t) sin(pi/4) ]
= sqrt(2) cos(2t+pi/4)
The rest should be easy for you.