An object having mass m is initially at rest on a frictionless horizontal surface. At time...

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An object having mass m is initially at rest on a frictionless horizontal surface. At time t = 0; a force is applied horizontally to the object, causing it to move in the positive x-direction. The force, in Newtons, is given by f(t) = 12t. (a) Given that velocity is the change in displacement with respect to time and the acceleration is the change in velocity with respect to time. State a second order ordinary differential equation and two initial conditions of this problem. (Hint: The net force on an object is equal to the mass of the object multiplied by the acceleration of the object) (b) Let m = 1 kg. Using Laplace Transform, find the velocity, and the displacement, x of the object at t = 2 seconds. An object having mass m is initially at rest on a frictionless horizontal surface. At time t = 0; a force is applied horizontally to the object, causing it to move in the positive x-direction. The force, in Newtons, is given by f(t) = 12t. (a) Given that velocity is the change in displacement with respect to time and the acceleration is the change in velocity with respect to time. State a second order ordinary differential equation and two initial conditions of this problem. (Hint: The net force on an object is equal to the mass of the object multiplied by the acceleration of the object) (b) Let m = 1 kg. Using Laplace Transform, find the velocity, and the displacement, x of the object at t = 2 seconds.

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a Second order ordinary differential equation The net force acting on the object is equal to the mas... View the full answer