Consider a sine wave signal of 80 Hz. 1024 data points are taken at a sampling frequency of 400 Hz. Calculate the total sampling time, frequency resolution, and the maximum useful frequency.

What is the heat treatment of metals? what is the benefit of it? why and how it's useful? answer in details, do not write by hand.

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?

Brief discuss how the presence of dislocations in crystal structures can be an advantage and a disadvantage to engineer and designers.