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
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 explanationLog 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
The following second-order linear differential equations model the vibrations of a spring-mass system: Equation (1): 49 𝑦 ″ + 42 𝑦 ′ + 9 𝑦 = 0 Equation (2): 16 𝑦 ″ + 9 𝑦 = 0 Equation (3): 10 𝑦 ″ + 37 𝑦 ′ + 7 𝑦 = 0 Equation (4): 𝑦 ″ + 6 𝑦 ′ + 58 𝑦 = 0 The motion of the spring modeled by Equation (1) is classified as [ Select ] an overdamped motion a simple harmonic motion. an underdamped motion. a critically damped motion . The motion of the spring modeled by Equation (2) is classified as [ Select ] a critically damped motion an overdamped motion a simple harmonic motion an underdamped motion . The motion of the spring modeled by Equation (3) is classified as [ Select ] a simple harmonic motion an overdamped motion a critically damped motion an underdamped motion . The motion of the spring modeled by Equation (4) is classified as [ Select ] an underdamped motion an overdamped motion a simple harmonic motion a critically damped motion .
In a consumer society, many adults channel creativity into buying things
Economic stress and unpredictable times have resulted in a booming industry for self-help products
People born without creativity never can develop it
More Practical Tools for Students Powered by AI Study Helper
Making Your Study Simpler
Join us and instantly unlock extensive past papers & exclusive solutions to get a head start on your studies!