When the vibrations of a string are damped, with a resistance which is proportionnal to the...

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When the vibrations of a string are damped, with a resistance which is proportionnal to the velocity. the one dimmensional wave equation becomes Pu Ət² Ju Ət 01² where is the constant of proportionality and is the wave speed. +2k a. If the initial shape of the string sin (at any point ) and the constant of proportionality is half. Write down the initial boundary value problem that describes the damped vertical vibrations u(x, t) of a string of length which is fixed at both ends and initially at rest, and unit wave speed. (10 Marks) b. Determine the vibrations of the string at each point and at time t, by solving the initial problem obtained in part (a.). (15 Marks) When the vibrations of a string are damped, with a resistance which is proportionnal to the velocity. the one dimmensional wave equation becomes Pu Ət² Ju Ət 01² where is the constant of proportionality and is the wave speed. +2k a. If the initial shape of the string sin (at any point ) and the constant of proportionality is half. Write down the initial boundary value problem that describes the damped vertical vibrations u(x, t) of a string of length which is fixed at both ends and initially at rest, and unit wave speed. (10 Marks) b. Determine the vibrations of the string at each point and at time t, by solving the initial problem obtained in part (a.). (15 Marks)

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The given damped wave equation is ut 2k ut c ux Here ut represents the second partial derivative of u with respect to time t ut represents the first p... View the full answer