Obtain the natural frequencies and mode shapes for a free-free uniform beam in lateral vibration and plot the first three modes. ignore the rigid-body modes

Coiled springs ought to be very strong and stiff. si3n4 is a strong, stiff material. would you select this material for a spring? explain.

Ariver flows from north to south at 8 km/h. a boat is to cross this river from west to east at a speed of 20 km/h (speed of the boat with respect to the earth/ground). at what angle (in degrees) must the boat be pointed upstream such that it will proceed directly across the river (hint: find the speed of the boat with respect to water/river)? a 288 b. 21.8 c. 326 d. 30.2

How to increase the thermal officiency of an ideal simple rankino cycle? among these methods, which one is the best and why?