solve in series the equation d2y/dx2+x2y = 0
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This is the equation of motion of S H M or simple harmonic motion. It is applicable for oscillations of a mass m attached at the end of a spring whose other end is tied to a wall or a rigid body. The same equation is applicable in a circular motion also.
It is the equation of motion of a pendulum.
Let y = A sin (ωx +Ф)
y' = d y/ d x = Aω cos (ωt + Ф)
y" = d² y / d x² = - A ω² sin (ω t + Ф ) = - A ω² y
So A = 1 and the solution is y = Sin (ω t + Ф)
This is the equation of motion of S H M or simple harmonic motion. It is applicable for oscillations of a mass m attached at the end of a spring whose other end is tied to a wall or a rigid body. The same equation is applicable in a circular motion also.
It is the equation of motion of a pendulum.
Let y = A sin (ωx +Ф)
y' = d y/ d x = Aω cos (ωt + Ф)
y" = d² y / d x² = - A ω² sin (ω t + Ф ) = - A ω² y
So A = 1 and the solution is y = Sin (ω t + Ф)
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