1. A 1 kilogram mass is attached to a spring with a springconstant of 4 N/m. Write the equation of motion if the spring isstretched 25 cm below the equilibrium position and released.
a) Suppose the system experiences a constant forcing functiondownwards of 4 N. (Note that one would need to divide by the mass,but the mass is 1 kg so we don’t see a difference here.) Solve thenon-homogeneous equation. (Keep everything else about the initialvalue problem the same.) How does the forcing function change thesolution/motion?
b) Suppose the forcing function is the periodic function ?(?) =4 cos ?. Solve that nonhomogeneous equation. What is the period andamplitude of the motion in this system?
c) Suppose the forcing function is the periodic function ?(?) =4 cos 2?. Solve this nonhomogeneous equation. How does the periodand amplitude of the motion change? How would you describe themotion?
