(5 points) let’s investigate with a test problem (a problem where we know the exact answer). approximate f 0 (1) for f(x) = x 2 sin(x) using a centered difference. in matlab, create an array called h. start with h(1)=0.05. in a while loop, decrease the step size by a factor of 2 each time until h(i) is smaller than 10−13 . build another array error in the same loop containing the exact errors for each approximation. create a log-log plot of the results with the command

An engine, weighing 3000 n, is supported on a pedestal mount. it has been observed that the engine induces vibration into the surrounding area through its pedestal at the maximum operating speed. determine the stiffness of the dynamic vibration absorber spring in (n/m) that will reduce the vibration when mounted on the pedestal. the magnitude of the exciting force is 250 n, and the amplitude of motion of the auxiliary mass is to be limited to 2 mm note: in this question type-in right numbers, no decimals, no fractions, no unit. approximate to right number if needed