1. A 1 kilogram mass is attached to a spring with a spring constant of 4...

1. A 1 kilogram mass is attached to a spring with a spring constant of 4 N/m. Write the equation of motion if the spring is stretched 25 cm below the equilibrium position and released.

a) Suppose the system experiences a constant forcing function downwards 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 the non-homogeneous equation. (Keep everything else about the initial value problem the same.) How does the forcing function change the solution/motion?

b) Suppose the forcing function is the periodic function ?(?) = 4 cos ?. Solve that nonhomogeneous equation. What is the period and amplitude 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 period and amplitude of the motion change? How would you describe the motion?

Expert Solution

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genius_generous answered 2 years ago

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