Question

A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released from rest from a point 6 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1 2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t)

Answer 1

The question involves setting up a differential equation for a mass on a spring undergoing damped Simple Harmonic Motion with an external driving force, to find the equation of motion, x(t).

Step-by-step explanation:

The question deals with a mass attached to a spring experiencing Simple Harmonic Motion (SHM) with damping and an external driving force. The mass is subject to a damping force that is proportional to its velocity and is influenced by an external force f(t). Using Hooke's law for spring force, Newton's second law for motion, and considering the damping force, we can set up a differential equation to describe the motion of the mass. This differential equation will have terms representing the restoring force from the spring, the damping force, and the driving force. Solving this differential equation will provide us with the equation of motion x(t) for the oscillating system.