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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define what a steady-state solution is in the context of damped harmonic motion.
π‘ Hint: Think about how the system responds after initial disturbances.
Question 2
Easy
What is the formula for phase difference (Ξ΄)?
π‘ Hint: It relates to the damping ratio and the frequencies.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What happens to a damped harmonic oscillator under a periodic force over time?
- It stops moving
- It oscillates at a different frequency
- It eventually oscillates at the same frequency as the force
π‘ Hint: Consider the definition of steady-state solution.
Question 2
True or False: The amplitude decreases infinitely when damping is high.
- True
- False
π‘ Hint: Think about how energy input balances losses.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A damped harmonic oscillator with m = 2 kg, k = 200 N/m, and a damping coefficient b = 10 Ns/m is subjected to an external force Fβ = 100 N. Calculate the steady-state amplitude at a driving frequency of 10 Hz.
π‘ Hint: Make sure to convert frequency to angular frequency.
Question 2
Explain how the characteristics of a system change when damping is critically damped vs. underdamped with a fixed external force.
π‘ Hint: Consider what happens with increasing damping in terms of oscillation characteristics.
Challenge and get performance evaluation