3. "The Dance of the Pendulum" represents the scientific principle that:
a. The kinetic and gravitational potential energies are both constant.
b. The kinetic and gravitational potential energies are equal at all times.
c. The maximum gravitational potential energy is achieved when the mass passes through its equilibrium
position.
d. The total mechanical energy is constant.
e. The maximum kinetic energy occurs at maximum displacement of the mass from its equilibrium position

d) The total mechanical energy is constant.

Explanation:

The total mechanical energy of a pendulum is given by:

where

KE is the kinetic energy (the energy of motion), given by

where

m is the mass of the pendulum

v is its speed

PE is the potential energy of the pendulum (the energy due to its position), given by

where

g is the acceleration due to gravity

h is the height of the pendulum relative to the ground

In absence of air resistance, the total mechanical energy of the pendulum is constant. This means that there is a continuous conversion of energy between kinetic and potential. In particular:

- When the pendulum is at its highest position (maximum displacement), the potential energy is maximum while the kinetic energy is minimum)

- When the pendulum crosses its equilibrium position, the kinetic energy is maximum (maximum speed) while the potential energy is minimum

explanation:

wheres the pic