Questions
Questions

SMAT011 Weekly Quiz 9 |LA009

Multiple dropdown selections

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 .

View Explanation

View Explanation

Verified Answer
Please login to view
Step-by-Step Analysis
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

Log in for full answers

We've collected over 50,000 authentic exam questions and detailed explanations from around the globe. Log in now and get instant access to the answers!

Similar Questions

More Practical Tools for Students Powered by AI Study Helper

Join us and instantly unlock extensive past papers & exclusive solutions to get a head start on your studies!