Final Answer:
The period of oscillation for the block pulled down an additional distance of 0.668 m and released from rest, is approximately T = 2π√(m/k), where m is the mass of the block and k is the spring constant.
Step-by-step explanation:
When the block is pulled down and released, it undergoes simple harmonic motion (SHM). The formula for the period (T) of an object undergoing SHM is given by T = 2π√(m/k), where m is the mass and k is the spring constant. In this case, the additional distance of 0.668 m doesn't affect the equilibrium position, but it does impact the amplitude of oscillation.
The key insight here is that the period of oscillation in simple harmonic motion depends only on the mass and the spring constant, not on the amplitude. Thus, the given period is determined solely by the initial conditions of the system, specifically the mass of the block and the spring constant. The formula T = 2π√(m/k) encapsulates this relationship, providing a straightforward way to calculate the period.
In summary, the period of oscillation is determined by the interplay between the mass of the block and the spring constant, as given by the formula T = 2π√(m/k). The additional distance of 0.668 m, while affecting the amplitude, does not alter the period of oscillation in this scenario.