A real continuous-time signal xc(t) is bandlimited to frequencies below 5 kHz; i. e., Xc(jΩ) = 0 for |Ω| >= 2π(5000). The signal xc(t) is sampled with a sampling rate of 10,000 samples per second (10 kHz) to produce a sequence x[n] = xc(nT ) with T = 10−4. Let X[k] be the 1000-point DFT of x[n].

a. To what continuous-time frequency does the index k = 150 in X[k] correspond?
b. To what continuous-time frequency does the index k = 800 in X[k] correspond?

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