Consider the following 2nd order ODE, where the prime (\') denotes differentiati

Question

Consider the following 2nd order ODE, where the prime (') denotes differentiation, with respect to time (mL^2) theta" + (ka^2 + mgL) theta = A cos(omega t). defining, y1 = theta, the appropriate coupled ODEs obtained by reduction of order are: (a) y1' - y2 and y2' = -(ka^2 + mgL)y1 + A cos (omega t) (b) y1' = y2 + A cos (omega t) and y2' = -(ka^2 + mgL)y1/mL^2 (c) y2' = y1 and y1' = [A cos (omega t) - (ka^2 + mgL)y2]/mL^2 (d) y1' - y2 and y2' = [A cos (omega t) - (ka^2 + mgL)y1]/mL^2 (e) none of the above

Explanation / Answer

Consider the following 2nd order ODE, where the prime (') denotes differentiation, with respect to time (mL2) theta" + (ka2 + mgL)theta = Acos(wt) defining, yl= theta, the appropriate coupled ODE's obtained by reduction of order are:

Answer:

(d) y1' = y2 and y1' = [Acos(wt) - (ka^2+mgL)y2] / mL^2

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