Solve: d^2x//dt^2 + g sin theta t =0 if theta=g//l , and g and l are constants?
2 Answers
Apr 27, 2018
Explanation:
You are asking for the solution to:
Apr 28, 2018
x = l^2/g \ sin theta t + At + B
Explanation:
We have:
(d^2x)/(dt^2) + g sintheta t = 0 wheretheta=g/l , a constant
Which we can write as:
(d^2x)/(dt^2) = - g sintheta t
We can "separate the variables" , to get:
(dx)/(dt) = int \ - g sintheta t \ dt
And integrating give us:
(dx)/(dt) = g/theta cos theta t + A
And repeating we get:
x = int \ g/theta cos theta t + A \ dt
So that:
x = g/theta^2 sin theta t + At + B
\ \ = g/(g/l)^2 sin theta t + At + B
\ \ = g l^2/g^2 \ sin theta t + At + B
\ \ = l^2/g \ sin theta t + At + B
