题目

SMAT011 Weekly Quiz 9 |LA009

多重下拉选择题

The following second-order homogeneous linear differential equations model the vibrations of a spring-mass system: Equation (1): 36 𝑥 ″ + 60 𝑥 ′ + 25 𝑥 = 0 Equation (2): 49 𝑥 ″ + 4 𝑥 = 0 Equation (3): 18 𝑥 ″ + 21 𝑥 ′ + 5 𝑥 = 0 Equation (4): 49 𝑥 ″ + 14 𝑥 ′ + 5 𝑥 = 0 The motion of the spring-mass system modeled by Equation (1) is classified as [ Select ] Underdamped motion Free undamped motion Critically damped motion Overdamped motion . The motion of the spring-mass system modeled by Equation (2) is classified as [ Select ] Underdamped motion Overdamped motion Critically damped motion Free undamped motion . The motion of the spring-mass system modeled by Equation (3) is classified as [ Select ] Underdamped motion Critically damped motion Overdamped motion Free undamped motion . The motion of the spring-mass system modeled by Equation (4) is classified as [ Select ] Overdamped motion Underdamped motion Critically damped motion Free undamped motion .

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思路分析

We are classifying each second-order homogeneous linear differential equation a x'' + b x' + c x = 0 in terms of damping: - Underdamped: oscillatory motion with decaying amplitude (complex roots, b^2 < 4ac). - Critically damped: fastest non-oscillatory return to equilibrium (repeated real root, b^2 = 4ac). - Overdamped: non-oscillatory return to equilibrium, but slower than critical (distinct......Login to view full explanation