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.

(01.02 mc) asap plzzzwhich of the following correctly simplifies the expression 3 to the power of 2 multiplied by 5 to the power of 0 whole over 4, the whole squared.? select one: a. 3 to the power of 2 multiplied by 1 whole over 4, the whole squared. = 3 to the power of 1 multiplied by 1 squared over 4 squared. = 1 over 6.b. 3 to the power of 2 multiplied by 0 whole over 4, the whole squared. = 3 to the power of 4 multiplied by 0 over 4 squared. = 0c. 3 to the power of 2 multiplied by 0 whole over 4, the whole squared. = 3 to the power of 1 multiplied by 0 over 4 squared. = 0d. 3 to the power of 2 multiplied by 1 whole over 4, the whole squared. = 3 to the power of 4 multiplied by 1 squared over 4 squared. = 81 over 16.