A spring-mass-damper system has the following equilibrium equation: d²y dy 4 +3 +40y = 0, t>0 dt? dt where y(t) = displacement in meters, and t = time in seconds. (3-a) Determine the general solution of y(t). (3-b) Assuming y(0) = 0 and y'(0) = 1, determine the particular solution of y(t). (3-c) Use Laplace transform to solve the given differential equation with the same initial conditions in (3-6)

A spring-mass-damper system has the following equilibrium equation: d²y dy 4 +3 +40y = 0, t>0 dt? dt where y(t) = displacement in meters, and t = time in seconds. (3-a) Determine the general solution of y(t). (3-b) Assuming y(0) = 0 and y'(0) = 1, determine the particular solution of y(t). (3-c) Use Laplace transform to solve the given differential equation with the same initial conditions in (3-6)