Final Answer:
The equation of motion for the given mass-spring system, described by the differential equation 2y" + 10y = 40sin(2t), is a second-order linear differential equation.
Step-by-step explanation:
The provided differential equation, 2y" + 10y = 40sin(2t), represents the motion of a mass-spring system. This second-order linear differential equation describes the relationship between the displacement of the mass (y) and its acceleration (y") with respect to time (t). The term "2y" represents the second derivative of y with respect to t (y"), while the term "10y" corresponds to the displacement y itself.
The right-hand side of the equation, 40sin(2t), represents an external force or input acting on the system. In this case, the force is a sinusoidal function, 40sin(2t), with a frequency of 2 and an amplitude of 40.
To determine the equation of motion, one would typically solve this differential equation using the given initial conditions, y(0) = -0.375 and y'(0) = 1.5. This solution would provide the specific equation that describes the displacement of the mass as a function of time, considering both the inherent properties of the system and the applied force.
By solving this differential equation with the initial conditions, the precise equation that governs the motion of the mass-spring system under the given conditions can be determined.