Application of second order ODE A 2 kg mass is attached to a

A 2 kg mass is attached to a spring with stiffness 20 N/m. The damping constant for the system is 12 N-sec/m. If the mass is pulled 2 m to the right of equilibrium and given an initial leftward velocity of 8m/sec. Find the equation of motion of the mass. When will the mass first return to its equilibrium position?

Solution

Solution :

(a)

The equation of motion of the mass :

[mass]y\'\'+ [damping]y\' + [stiffness]y = 0

So, our initial value problem becomes :

2y\'\' + 12y\' + 20y = 0 , y(0) = 2, y\'(0) = - 8

This has the solution :

y = 2e^-3x( cos(x) - sin(x))