க 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) = 30 sin(6t) Newtons. a. Solve the initial value problem. y(t)= 887 help (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. That is, at least some of the terms in the formula go to zero, and those terms are called transient terms. The asymptotic approximating function will not include those transient terms. For very large positive values of t, y(t) ≈0 help (formulas)

Q: 1 (a) Draw a direction field and sketch a few trajectories. (b) Describe how the solutions behave as…

A:

Q: (c) 2ry'y-y²+²=0.

A: 2xy'y-y2+x2=0⇒2xyy'=y2-x2

Q: Solve y"+y'-2y=0,y(0)=4,y'(0)=1

A:

Q: 8. feet. The mass is initially released from rest from a point 3 feet below the equilibrium…

A:

Q: A model for the velocity v at time t of a certain object falling under the influence of gravity in a…

A: From the solution draw the graph on the direction field.

Q: 5 An object moves along the y-axis with the coordinate position y(t) and velocity v(t) = Vt- cos(e)…

A: We have to check

Q: A 1 kg mass is attached to a spring with a spring constant k = 9N/m. A periodic force F(t) = cos(wt)…

A:

Q: 5) Particle motion At time t≥0, the velocity of a body moving along the horizontal s-axis is v = t²…

A: At time t ≥ 0, the velocity of a body moving along the horizontal x-axis is v(t) = t2 − 4t + 3. Now…

Q: ('. frictionless spring with a 7-kg mass can be held stretched 0.2 meters beyond its natural length…

A: