19.8.2 - Example 2: Initial Displacement Only
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What does initial displacement refer to in a vibrating membrane?
💡 Hint: Think about how the shape of the membrane is defined at the starting point.
What happens to the coefficients B_nm when the initial velocity is zero?
💡 Hint: Consider the implications of starting from rest.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is set to zero in this example to simplify the model?
💡 Hint: Consider how the static start affects the vibration pattern.
The function A_nm represents what aspect of the vibration?
💡 Hint: Think about how initial conditions influence vibrational behavior.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
A rectangular membrane of dimensions 1m x 2m is initially displaced according to f(x,y) = x + y. Calculate A_11.
💡 Hint: Set up the integrals carefully and solve them step by step.
Consider a two-dimensional membrane with non-zero initial velocity as well as initial displacement. How would you handle the calculation of A_nm and B_nm together?
💡 Hint: Think about the individual contributions of both conditions to the overall behavior.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.