Solve the differential equation?

Question

solve the differential equation d^2 x/dt^2 =k.cosx

Answer 1

Are u sure the RHS is cos x, not cos t

Answer 2

d^2x/dt^2 =kcosx

take x =pi.wt/2

we known that k is const

so

dx/dt = k pi.w/2* (sin pi.wt/2)

again integrate

X = k (pi.w/2)^2[-cos pi.wt/2]

or X= k (pi.w/2)^2[-cosx]