Please see attached for question and diagram.
A certain engineering system can be represented by mass in a spring, as shown in Figure 1. If the mass is pulled downwards and then released, it oscillates on the spring. Using Newton's second law, a homogeneous second-order differential equation can be set up as below (see attached).© BrainMass Inc. brainmass.com March 4, 2021, 8:19 pm ad1c9bdddf
Oscillatory motion of a spring mass system is called Simple Harmonic Motion. I have solved the equation of motion of a oscillating spring mass system using the given boundary conditions.