Tutorial__10 - Tutorial 10 The motion of a violin string...

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Tutorial # 10 # The # motion # of # a # violin # string # under # tension # is # governed # by # the # wave # equation, # including # a # damping # force # term: # PDE: # ߲ ݏ ߲ݐ ൌ ܽ ߲ ݏ ߲ݔ െ ݇ ߲ݏ ߲ݐ # where # ܽ # and # ݇ # are # known # constants. # # BCs: # ݏሺݔ ൌ Ͳǡ ݐሻ ൌ Ͳ ## and ## ݏሺݔ ൌ ܮǡ ݐሻ ൌ Ͳ # i.e. # fixed # ends # ICs: # ݏሺݔǡ ݐ ൌ Ͳሻ ൌ Ͳ ## and ## డ௦ డ௧ ሺݔǡ ݐ ൌ Ͳሻ ൌ ݃ሺݔሻ # Where # ݃ሺݔሻ # is # a # specified # velocity. # i.e. # the # vibrations # are # started # by # giving # the # string # an # initial # velocity, # while # it # is # in # the # equilibrium # position. # Suppose # that # ݃ሺݔሻ ൌ ܸ
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