Newton's Cradle, Simple Harmonic Motion

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Newton's Cradle can be analyzed as a system exhibiting simple harmonic motion, particularly if the spheres are treated as point masses. The period of the cradle is akin to that of a simple pendulum, which remains constant regardless of mass. The center of mass maintains a consistent velocity throughout the collisions, allowing the cradle to be viewed as a single oscillating mass. The calculations for the period can be derived using the appropriate equations for pendulum motion. Overall, Newton's Cradle effectively demonstrates principles of simple harmonic motion under ideal conditions.
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Is it possible to see Newton's cradle in simple harmonic motion?

Im thinking that the period is the same as a simple pendulum, if not how would I calculate this?
 
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It is simple harmonic motion as long as you pretend that the five spheres are point masses. The velocity of the center of mass does not change through the multiple collisions, so you can view this as a single oscillating mass. Since the period of a simple pendulum is independent of the mass, then it is given by an equation that looks like ...
 

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