Explain, with reasons, whether the LTIC systems described by the following differential equations are (i) stable or unstable in the BIBO sense) asymptotically stable, unstable, or marginally stable. Recall that the symbol D stands for , while D2 for (a) (D +8D 12)y(t) (D 1)(t). (b) D(D23D +2)y(t) (D5)(t) (c) D2(D2+2)y(t)=x(t). (d) (D1)(D2 6D 5)y(t) (3D1(t)

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?

What is the correct way to measure the overall length of a boat? measure from the tip of the bow to the highest point on the gunwale. measure from the tip of the bow in a straight line to the stern of the boat. measure from the tip of the bow in a straight line to the back seat. measure from port to starboard at the boat's widest point.

Consider two concentric spheres forming an enclosure with diameters of 12 cm and 18 cm the spheres are maintained at uniform temperatures ti-50°c and t2 = 250°c and have emissivities .45 and .8, respectively. determine the net rate of radiation heat transfer between the two spheres per unit surface area.