Amass m attached to a horizontal massless spring with spring constant k, is set into simple harmonic motion. its maximum displacement from its equilibrium position is a. what is the masses speed as it passes through its equilibrium position?

At the point of maximum displacement (a), the elastic potential energy of the spring is maximum:

while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:

And the total energy of the system is


Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:

while the mass is moving at speed v, and therefore the kinetic energy is

And the total energy is


For the law of conservation of energy, the total energy must be conserved, therefore . So we  can write

that we can solve to find an expression for v:

The charge of an ion with 55 protons and 52 electrons is +3. the reason is because protons are positive, and there are three more than the amount of negative electrons.