Consider the initial value problem my′′+cy′+ky=f(t), y(0)=0, y′(0)=0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force f(t), where the unit of force is the newton (n). assume that m=2 kilograms, c=8 kilograms per second, k=80 newtons per meter, and f(t)=30sin(6t) newtons.1. solve the initial value problem. y(t)=? 2. determine the long term behavior of the system.

Which of the following would be a correct step in proving that triangle abc is congruent to triangle cda? a. use a protractor to measure the angles and show that all the corresponding angles are equal in measure. this will allow you to prove congruence by aaa. b. show that segment ab is parallel to segment cd and segment ad is parallel to segment cb. this will allow you to prove congruency by asa. c. show that is segment ab is perpendicular to segment ad. this will allow you to prove congruence by sas. d. none of the above.