Hello, Just for curiosity... Is Hooke's law valid for a vibrating massive spring ? I have done some calculations using both Newton's 2nd Law and the conservation of energy to a horizontal swinging spring connected to a small block in the absence of any friction. I have found that the tension of the spring depends on both the elongation and the acceleration. However, the acceleration is multiplied by the mass of the spring, so if the spring is massless, the tension is reduced to T = kx. Here is the outline of my work: >> I have written the expression of the mechanical energy of the system (block-spring), and then set the derivative to zero. I concluded at the end that I can neglect the mass of the spring if I assume the mass of the block is M + m/3 where m is the mass of the spring and M is the mass of the block. I checked this out on the internet, and I found this conclusion true. >> Next I have applied Newton's 2nd Law: For a massless spring: T = Ma For a massive spring, the tension is T': T' = (M + m/3)a (Neglect the mass of the spring and add its third to the block) T' = Ma + ma/3 T' = T + ma/3 T' = -kx + ma/3 (Note that the tension depends on the acceleration). Is my work correct? Thank you.