Suppose we have a mass spring system with a mass of 2 kg, a damping constant of
ID: 3286589 • Letter: S
Question
Suppose we have a mass spring system with a mass of 2 kg, a damping constant of b= 4 kg/sec, and a spring constant of 12 kg/sec^2. Suppose this system is forced with a force of f(t) = 8cos3 Newtons. The system is started in motion with the mass located 3 meters above the equilibrium position with an initial velocity of 2 m/s in the upward direction with upward positive. Find the differential equation and initial conditions that describe the motion of this system. Do not solve the initial problem.Explanation / Answer
the differential equation for a forced vibrating system is of the form mx'' + bx' + kx = f(t) x'' is the double differentiation of displacement x from the mean position putting the values of m b and k from the given question 2x'' + 4x' + 12x = 8 cos 3t