Question

1. y''+5y'+6y=12t+46y??+5y?+6y=12t+46
y(0)=13, y'(0)=?16y(0)=13, y?(0)=-16

2. Suppose the equation x''+169x=f(t)x??+169x=f(t) models a spring-mass system with forcing function f(t)f(t). Choose all possible forcing functions that would cause resonance in the system.

f(t)=9sin(169t)f(t)=9sin(169t)

f(t)=15cos(13t)f(t)=15cos(13t)

f(t)=2cos(169t)+15sin(169t)f(t)=2cos(169t)+15sin(169t)

f(t)=11cos(169t)f(t)=11cos(169t)

f(t)=14sin(13t)f(t)=14sin(13t)

f(t)=17cos(2t)f(t)=17cos(2t)

f(t)=10sin(2t)f(t)=10sin(2t)

f(t)=9sin(13t)?11cos(13t)