4.3.3. A square membrane with sides of length L, uniform surface density ps, and uniform tension T is fixed on three sides and free on the other. (a) Find the frequency of the fundamental mode. (b) Write a general expression for the natural frequencies and one for the normal modes. (c) Sketch the nodal patterns for the three normal modes with the lowest natural frequencies.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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**4.3.3.** A square membrane with sides of length \( L \), uniform surface density \( \rho_s \), and uniform tension \( \mathcal{T} \) is fixed on three sides and free on the other.

**(a)** Find the frequency of the fundamental mode.

**(b)** Write a general expression for the natural frequencies and one for the normal modes.

**(c)** Sketch the nodal patterns for the three normal modes with the lowest natural frequencies. 

There are no graphs or diagrams provided in this text.
Transcribed Image Text:**4.3.3.** A square membrane with sides of length \( L \), uniform surface density \( \rho_s \), and uniform tension \( \mathcal{T} \) is fixed on three sides and free on the other. **(a)** Find the frequency of the fundamental mode. **(b)** Write a general expression for the natural frequencies and one for the normal modes. **(c)** Sketch the nodal patterns for the three normal modes with the lowest natural frequencies. There are no graphs or diagrams provided in this text.
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