Solve the differential equation problem. b) An undamped oscillation under the influence of external force is given

Solve the differential equation problem.

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b) An undamped oscillation under the influence of external force is given by + kr = F(t), m- dt2 %3D where r(t) is the displacement at time t. Suppose a spring has mass m and spring constant k and let w with external force F(t) = Fo cos (wot), where wo # w. What type of value k and m so that the corresponding homogeneous solution is SO Th(t) = A cos(wt) + B sin(wt)? Hence, by using the method of undetermined coefficients, show that Fo x(t) = A cos(wt) + B sin(wt) + cos (wot). m(w? – wi) b) An undamped oscillation under the influence of external force is given by + kr = F(t), m- dt2 %3D where r(t) is the displacement at time t. Suppose a spring has mass m and spring constant k and let w with external force F(t) = Fo cos (wot), where wo # w. What type of value k and m so that the corresponding homogeneous solution is SO Th(t) = A cos(wt) + B sin(wt)? Hence, by using the method of undetermined coefficients, show that Fo x(t) = A cos(wt) + B sin(wt) + cos (wot). m(w? – wi)