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2 cards from this section. Quick, good the night before a test.
What is orthogonality in the context of sine functions?
Think about how perpendicular functions behave.
What is the value of the integral of sin(mx) * sin(mx) over [0,a]?
Refer to the self-product of sine functions.
What does the integral of sin(mx) * sin(nx) equal over [0,a] if m ≠ n?
Think about the property of orthogonal functions.
True or False: The integral of sin(mx) * sin(mx) over [0,a] equals a.
Review how squares of functions behave under integration.
Given the sine functions sin(2πx) and sin(3πx), calculate their integral over the interval [0,1] and explain the significance.
Remember to use the integral properties of sine functions.
Demonstrate how the orthogonality of sine functions aids in constructing a solution for a vibrating rectangular membrane.
Consider how modes interact during vibration and their independence.
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