Final answer:
The block on the frictionless surface reaches its maximum speed as it passes through the equilibrium position, where x = 0. The speed is calculated using the potential energy stored in the spring when the block is displaced and converting it into kinetic energy as the block moves through equilibrium.
Step-by-step explanation:
Understanding the Maximum Speed in Simple Harmonic Motion
In the context of simple harmonic motion (SHM) involving a mass attached to a spring on a frictionless surface, the point at which the speed of the block is at its maximum is when the block passes through the equilibrium position, also denoted as x = 0. At this position, the entire energy of the system is kinetic, as potential energy stored in the spring is zero.
The potential energy in the spring when the block was released and the spring was compressed by 12 cm is calculated using the formula for elastic potential energy U = (1/2)kx^2, where k is the spring constant and x is the displacement from equilibrium. Therefore, the potential energy U stored in the block-spring support system when the block was just released is U = (1/2)(100 N/m)(0.12 m)^2 = 0.72 Joules.
The speed of the block when it passes through the equilibrium position is found by converting this potential energy entirely into kinetic energy. The kinetic energy formula KE = (1/2)mv^2 allows us to solve for v, giving us the speed of the block as it passes through equilibrium. The mass m of the block is 300 g, which is 0.3 kg in SI units. Solving for speed, we get v = sqrt((2*U)/m) = sqrt((2*0.72 J)/(0.3 kg)) = 2.45 m/s.