Now let us consider a spring-mass system with more details. Consider a block of mass M hanging from the end of a vertical spring of un-stretched length L and a dashpot damper with damping coefficient c. Section 3.4 Copyright©Arunabha Biswas 163 Section 3.4 Copyright©Arunabha Biswas 164 Section 3.4 Copyright©Arunabha Biswas 165 Exercise: Consider a mass of 0.5 kg with spring constant k = 2 N/m in an undamped, unforced mass-spring system. Assume the mass is displaced 0.4 m from equilibrium and released. Describe the long term behavior of the system. Section 3.4 Copyright©Arunabha Biswas 166 Section 3.4 Copyright©Arunabha Biswas 167 Oscillating Solutions: sin/cos and Shifted-cos Forms Remark: We can always write the general solution of an undamped unforced spring system in either of two forms: Section 3.4 Copyright©Arunabha Biswas 168 Problem: Explain how this relationship helps us to understand the behavior of solution when m comes in complex conjugate pairs. Section 3.4 Copyright©Arunabha Biswas 169