## Simple horizontal harmonic oscillator with spring that has a mass.

Hi,

Consider a block of mass M connected to a spring of mass m and stiffness k horizontally on a frictionless table. We elongate the block some distance, and then release it so that it now oscillates.

According to the theoretical study using energy methods, we see that the mass of the spring affects the motion of the block.

But if we apply Newton's 2nd law to the system formed of the block alone, the mass of the spring do not appear in the equation!!

Here it is: F = Ma then -kx = Ma then a=(-k/M)x where the weight and the normal reaction cancel each other.

As we see the mass of the spring does not appear in the equation.

My question is: Does the mass of the spring affect the motion of the block? and if yes, what is wrong in the way I have applied Newton's second law above?