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Exercise:
A damped oscillation is given by the differential ddot yt -omega_^ yt-delta dot yt Derive the equivalent system of first order differential s and the corresponding matrix.

Solution:
We roduce an additional function v_ytdot yt. The differential for the damped oscillation can then be written as a system of two s: dot yt v_yt dot v_yt -omega_^ yt - delta v_yt The corresponding matrix is bf A leftmatrix & -omega_^ & -deltamatrixright We can write the s as fracddtleftmatrixytv_ytmatrixright bf A leftmatrixytv_ytmatrixright
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Exercise:
A damped oscillation is given by the differential ddot yt -omega_^ yt-delta dot yt Derive the equivalent system of first order differential s and the corresponding matrix.

Solution:
We roduce an additional function v_ytdot yt. The differential for the damped oscillation can then be written as a system of two s: dot yt v_yt dot v_yt -omega_^ yt - delta v_yt The corresponding matrix is bf A leftmatrix & -omega_^ & -deltamatrixright We can write the s as fracddtleftmatrixytv_ytmatrixright bf A leftmatrixytv_ytmatrixright
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Differential equations
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damped oscillation, linear differential equation, matrix, oscillation
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ENG (English)
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Calculative / Quantity
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