Answer to Question #67350 in Classical Mechanics for John

Question

Show that the natural angular frequency of a system governed by the equation y '' + 900 π2 y = cos( omega1 * t) is omega = 30 π. This system has a natural frequency of 15 and a period of 2/30. The function g(t) = cos(omega1 * t) drives the system. If the driving function comes into phase with the natural frequency every 8 cycles, what is ω1 (there are two possibilities and you may choose either, but it's probably easier to think in terms of the greater of the two). I do not need to know how to solve the equation. I just need to know how to find the "two possibilities". (Omega_1)