Consider the initial value problem my" + cy' + ky = f(t), y(0) = 0, y'o) = 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) = 50 sin(6) newtons. a. solve the initial value problem. y(t) = (25/(6t)-6cos(6t))e^(2t)+sin(6t)+co s(6t))^(-2t) (formulas) b. determine the long-term behavior of the system. is lim y(t) = 0? if it is, enter zero. if not, enter a function that approximates y(t) for very large positive values of t. for very large positive values of t, y(t) t (formulas)

What are correct trigonometric ratios that could be used to determine the length of ln

Is δ pmr similar to δ smn ? if so, which postulate or theorem proves these two triangles are similar?

In new york city at the spring equinox there are 12 hours 8 minutes of daylight. the longest and shortest days of the year very by two hours and 53 minutes from the equinox in this year the equinox falls on march 21 in this task you use trigonometric function to model the hours of daylight hours on certain days of the year in new york city a.what is the independent and dependent variables? b.find the amplitude and the period of the function. c.create a trigonometric function that describes the hours of sunlight for each day of the year. d. graph the function you build in part c. e. use the function you build in part c to find out how many fewer daylight hours february 10 will have than march 21. you may look at the calendar.