Final answer:
The equation of motion for a mass driven by an external force can be determined using Newton's second law and integrating the acceleration with respect to time.
Step-by-step explanation:
The equation of motion for a mass driven by an external force can be determined using Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the external force is given by f(t) = 24 cos(2t) + 6 sin(2t). The mass of the object and its acceleration can be obtained from the equation a(t) = (f(t))/m, where m is the mass.
Substituting the given expression for f(t), we have a(t) = (24 cos(2t) + 6 sin(2t))/m. This equation represents the acceleration of the mass as a function of time.
To find the equation of motion, we need to integrate the acceleration with respect to time. Assuming the initial conditions (position, velocity) are known, the equation of motion can be found by integrating twice. The resulting equation will have the form y(t) = Acos(wt + p), where A, w, and p are constants determined by the initial conditions and the mass and external force.