The total energy of a particle executing S.H.M. is proportional to

Calculatipon:
The total energy of a particle executing Simple Harmonic Motion (S.H.M.) is given by the equation:

E = K + U

Where E is the total energy, K is the kinetic energy, and U is the potential energy.

For a particle in SHM, the kinetic energy is:

K = (1/2)mv²

And the potential energy is:

U = (1/2)kx²

The total energy (E) remains constant throughout the motion, and it is the sum of the kinetic and potential energies:

E = (1/2)kA²

Where A is the amplitude of the motion, and k is the spring constant.

Thus, the total energy is directly proportional to the square of the amplitude of the motion.

Correct Answer: Option 4 - square of amplitude of motion