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Question: How to solve for constants Deriving Simple Harmonic Motion?

Question:How to solve for constants Deriving Simple Harmonic Motion?

Ronan 1207 Maple 2016
constants differential-equation
January 22 2017
0

I am practicing with some diff equations. I am having problem solving for one of the constants. I am having a pproblem assigning a value to derivatives or 2nd derivatives. What is a good general technique is this type of situation?
 

restart

NULL

``

omega^2 = g/l

omega^2 = g/l

 (1)

Eq1 := diff(Theta(t), t, t) = -omega^2*Theta(t)

diff(diff(Theta(t), t), t) = -omega^2*Theta(t)

 (2)

ics := Theta(0) = 0, (diff(Theta(t), t))(0) = Vmax, (diff(Theta(t), t, t))(0) = 0

Theta(0) = 0, (diff(Theta(t), t))(0) = Vmax, (diff(diff(Theta(t), t), t))(0) = 0

 (3)

SHM := dsolve({Eq1, ics})

 (4)

SHM := dsolve({Eq1})

{Theta(t) = _C1*sin(omega*t)+_C2*cos(omega*t)}

 (5)

SHM := dsolve({Eq1, Theta(0) = 0})

Theta(t) = _C1*sin(omega*t)

 (6)

``

diffSHM := diff(SHM, t)

diff(Theta(t), t) = _C1*omega*cos(omega*t)

 (7)

``

(Theta(t))(0) = 0, (diff(Theta(t), t))(0) = V

(Theta(t))(0) = 0, (diff(Theta(t), t))(0) = V

 (8)

``

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NULL

NULL


 

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