Superposition of SHM: Adding Two Equations for Understanding

[andyrk]

Why do we simply add the equations of SHM in case the two SHMs are superimposing?

 

[Nugatory]

Are you familiar with the differential equation that describes a system undergoing simple harmonic motion, $x''=-kx$? If $x=A(t)$ and $x=B(t)$ are both solutions of that differential equation, then $x(t)=A(t)+B(t)$ is also a solution.

 

[Chestermiller]

Why do we simply add the equations of SHM in case the two SHMs are superimposing?

Because the differential equation is linear.

Chet