A Solve The Following Differential Equation 8 16y 9 Dy Dr2 Dz4 By Using The Method Of Undetermined Coetm 7 Marks B 1 (18.53 KiB) Viewed 21 times
a) Solve the following differential equation 8- +16y=9² dy dr2 dz4 by using the method of undetermined coeTM (7 marks) b) An undamped oscillation under the influence of external force is given by d'a diz+kz= za(t) -+ kr = F(t), where z(t) is where z(t) is the displacement at time t. Suppose a spring has mass m and spring constant k and let w with external force Focos (unt), where wow. What type of value k and m so that the corresponding homogeneous solution is F(t) = 1 cos(wt) + Bsin(wt)? Hence, by using the method of undetermined coefficients, show that Fo z(t) = Acos(ut) + B sin(wt) + m (w² − w) cos (wht).
a) Use partial fraction to find -¹ } - C-1 { 8² +10 +7 (8 + 1)(s² +8s+5) b) Given EM OUT H(s) = ind the value of constant kif Hence, find the inverse. 3 82(82+25) C-¹ {H(s)} = * k(t - u) sin (5u) du.
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