The spring constant can be determined from the oscillatory motion. For this case, Newton's second law gives
(md^2x)/(dt^2) + kx = 0
where x is the displacement from the equilibrium position. The sample mass is suspended from the spring by a sample holder.
Does m in this formula include the mass of the sample holder?
Yes, the holder's mass must be included, since it oscillates with its contents.
To determine whether the mass of the sample holder, m, should be included in the formula, we need to consider the physical system and what is being measured.
In the given formula (md^2x)/(dt^2) + kx = 0, 'm' represents the mass of the object that is oscillating, which in this case is the sample. The purpose of the formula is to describe the motion of the sample suspended from the spring.
Typically, the mass of the sample holder is not included in the 'm' term since the mass of the sample holder does not directly affect the motion of the sample. The sample holder only provides a means for suspending the sample from the spring.
Therefore, when determining the spring constant from the oscillatory motion, 'm' refers specifically to the mass of the sample being suspended from the spring and does not include the mass of the sample holder.