2. An object attached to the end of a spring is modeled by the ODE my" + by' + ky = Fexternal derived from Hooke's Law. y(t) is the displacement of the object from its equilibrium position (where the object naturally wants to be), m is the mass of the object, b is the damping coefficient, k is the spring constant, and Fexternal is an external force acting on the system. Write and solve the ODE using the Laplace Transform if the mass of the object is 1kg, the spring constant is 4, and the damping coefficient is 4 Ns. The object is struck by a hammer at time = 10 seconds. The initial displacement of the object is 1m, and the initial velocity of the object is 0. m

2. An object attached to the end of a spring is modeled by the ODE my" + by' + ky = Fexternal derived from Hooke's Law. y(t) is the displacement of the object from its equilibrium position (where the object naturally wants to be), m is the mass of the object, b is the damping coefficient, k is the spring constant, and Fexternal is an external force acting on the system. Write and solve the ODE using the Laplace Transform if the mass of the object is 1kg, the spring constant is 4, and the damping coefficient is 4 Ns. The object is struck by a hammer at time = 10 seconds. The initial displacement of the object is 1m, and the initial velocity of the object is 0. m