Question

A 5-kg mass is attached to a spring with stiffness 15 N/m. The damping constant for the system is 10V3 N-sec/m. If the mass is pulled 10 cm to the right of equilibrium and given an initial rightward velocity of 2 m/sec, what is the maximum displacement from equilibrium that it will attain? The maximum displacement is meters. (Type an exact answer, using radicals as needed.)

Answer 1

Here are here, mass of body maskg. stiffness of spring, ta 150/m. Damping constant for the system bagong beelm. when the mass is pulled to the right, the damping force acts towards eft (aren aurs) and force due to the spring also acts left. If the accennation is in the equation of motion of the system, is catenated from mnac Forfk.. - or mutabi akn lokka ke and mütbätkm ao forbi ) here, putting all raius : ců tlorn +15nao. - mo Now, 5 m it coram +15.0 şim Aron3 m +1500 ma mlora Id (100)? 4.5.15 (mo re) meine 2.5 The general solution of the ear ut) se ut ( 4 cosult it la sincet), where se ulice (soot of the cor) there warn, uso. ult) a gent ..() - arent.

mass is pulled to the right toon Now, the at tao. : 0.1 m i alt) = 01 metrat. the maximum displecement olma o from equibrum in
To calculate the maximum displacement from equilibrium we have to solve the equation of motion for damping oscillator as the spring mass system is a damping system.Using boundary conditions we can find the constant of the equation and we can find the maximum displacement.