Describe the variation of the net force on and the acceleration of a mass on a spring as it executes simple harmonic motion.

Hooke's law states that the force exerted by a spring is proportional to its displacement from equilibrium and acts in the opposite direction. It is given by: F = -kx, where F is the net force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.

Simple harmonic motion is a type of periodic motion where the restoring force acting on an object is directly proportional to its displacement from the equilibrium position and acts in the opposite direction. Mathematically, the acceleration of an object undergoing SHM can be written as: a = -ω^2x, where a is the acceleration, ω is the angular frequency, and x is the displacement from the equilibrium position.

Using Newton's second law of motion, we can write the net force acting on a mass m as: F = ma. We can then substitute the equation for the acceleration of the object undergoing SHM (a = -ω^2x) into the equation for net force: F = -mω^2x. Since the net force acting on the mass is the force exerted by the spring, we can write Hooke's law next to the equation for net force as F = -kx = -mω^2x.

From the above equations, we can observe that the net force acting on the mass is proportional to its displacement from the equilibrium position and acts in the opposite direction. The magnitude of the net force changes with the position of the mass, where it is maximum when the mass is farthest from the equilibrium position and zero when the mass is at the equilibrium position.

Since acceleration is directly proportional to the net force experienced by the mass (a = F/m), the acceleration of the mass will also change with its position. The acceleration will be maximum when the mass is farthest from the equilibrium position and zero when the mass is at the equilibrium position. The direction of the acceleration is always opposite to the direction of the displacement, causing the mass to return to the equilibrium position. In summary, as a mass on a spring undergoes simple harmonic motion, both the net force and acceleration vary with its position, always acting in the opposite direction to the displacement. The magnitude of net force and acceleration is maximum when the mass is farthest from the equilibrium position and zero when the mass is at the equilibrium position.