I just need help with numbers 5 through 6, I will give thumbs up. Thank you so much

45 pts 4. Find a general real solution of the equation y"+25y=20e' +2cos(5t) +tsin(5t) +sec(5t). 10:12 PM / 5. The vertical displacement of a mass on a spring is given by 10 pts h"+6h'+13h= a cos(wt) + Bsin(@t) where positive displacements are upward. (Assume a, B #0, @>0 . Assume CGS units.) (a) Is this system undamped, under damped, critically damped, or over damped? Explain why. (b) Give the natural frequency and period of the system. (c) Give the quasi period = damped period , quasi frequency = damped frequency. 10:13 PM / 6. When a 10 gram mass is hung vertically from a spring, at rest it stretches th spring 4.9 cm. (Gravitational acceleration is g =980cm/sec2 .) At t=0, the mass is displaced 5 cm below its rest position and is released with a downward velocity of 3 cm/sec. Assume that the spring force is proportion to displacement, that there is no damping and that the mass is driven by an external force of Few (t)=11cos(wt) dynes (1 dyne = 1 gram cm/sec? ), where upward displacements are taken to be positive. 10 pts (a) Formulate an initial value problem that governs the motion of the mass for t> 0. (Do NOT solve, just write it down) (b) What is the natural frequency @ of this spring? (c) At what value of the driving frequency @ does resonance occur