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Transcript
Homework 22
1. Find the general solution to
y (3) − 21y ′′ + 151y ′ − 291y = 0.
2. Determine the period T , the angular frequency ω0 , the amplitude C, and the phase angle
α for a mass of 4kg oscillating on a spring with k = 3 N/m with initial position x(0) = 1 and
initial velocity x′ (0) = −1.
3. Solve the initial value problem
y ′′ − y = ex + 3x + sin x, y(0) = 0, y ′(0) = 1.
4. Consider the equation
2x′′ + 3x = sin2 ωt.
For what values of ω does resonance occur?