How to Solve the Initial Condition Problem for Finding A_x and A_y Expressions?

[nhrock3]

i can't see how they got X and Y expressions
V_x is the derivative of X(t) by t
'A' and phi are needed to be found
but when i don't know how to innpur the initial condition to find A_x and A_y
because when we integrate x' expression bot sides i get
x(t)-x(0)=[A_x*cos(wt+phi)]/w - [A_x*cos(0+phi)]/w
so i can't put 'b' instead of x(0) but it doesn't give me A_x parameter value

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[tiny-tim]

hi nhrock3!

(pleeeeeeeeeeease don't post such wide pictures! )

i can't see how they got X and Y expressions
V_x is the derivative of X(t) by t

(have an omega: ω )

the general solution can be written either as cos(ωt + φ), or as Acosωt + Bsinωt …

the book uses the second method to get the constants

 

[nhrock3]

i only used the first
how to do the second?

 

[tiny-tim]

uhh? x(0) = A, x'(0) = ωB

 

[nhrock3]

why uhh? :)

 

[nhrock3]

ahh ok i understand

 

[nhrock3]

why i can't do it the first method
i want to solve it the irst way

 

[tiny-tim]

you can solve it the first way, it's just more difficult …

put t = 0 and chug away ​

 

[nhrock3]

i put t=0
and get that phi=0
what next?