Assignment:
Q1. A spring with a 4-kg mass has natural length 1 m and is maintained stretched to a length of 1.3 m by a force of 24.3 N. If the spring is compressed to a length of 0.8 m and then released with zero velocity, find the position of the mass at any time t.
Q2. Consider a spring with mass m, spring constant k, and damping constant c = 0, and let w = √(k/m). If an external force F(t) = F0 cos wt is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to show that the motion of the mass is given by x(t) = c1 cos ωt + c2 sin ωt + (F0/(2mω))t sin ωt.
Provide complete and step by step solution for the question and show calculations and use formulas.