Write the differential equation describingthe SHM of mass m attached to a spring offorce constant k.

To describe the simple harmonic motion (SHM) of a mass m attached to a spring with force constant k, we can start by considering Newton's second law of motion.

According to Newton's second law, the net force acting on an object is equal to the product of its mass and acceleration. In this case, the net force acting on the mass m is the force exerted by the spring, which can be given by Hooke's law.

Hooke's law states that the force exerted by a spring is directly proportional to the displacement of the mass from its equilibrium position. Mathematically, this can be expressed as F = -kx, where F is the force, k is the force constant of the spring, and x is the displacement of the mass from its equilibrium position.

Since acceleration is the second derivative of displacement with respect to time, we can write the equation of motion for the mass m as:

m * d^2x/dt^2 = -kx

This is the differential equation that describes the simple harmonic motion of a mass m attached to a spring with force constant k.