Suppose that a mass is initially at x= xo with an initial velocity vo. show that the resulting motion is the sum of two oscillations, one corresponding to the mass initially at rest at x= xo and the other corresponding to the mass initially at the equilibrium position with velocity va. what is the amplitude of the total oscillation ?

Apiston-cylinder with a volume of 0.25 m3 holds 1 kg of air (r 0.287 k/kgk) at a temperature of 100 c. heat transfer to the cylinder causes an isothermal expansion of the piston until the volume triples. how much heat is added to the piston-cylinder?

Two flowing streams of argon gas are adiabatically mixed to form a single flow/stream. one stream is 1.5 kg/s at 400 kpa and 200 c while the second stream is 2kg/s at 500 kpa and 100 ? . it is stated that the exit state of the mixed single flow of argon gas is 150 c and 300 kpa. assuming there is no work output or input during the mixing process, does this process violate either the first or the second law or both? explain and state all your assumptions.

Afluid flows with a velocity field given by v=(x/t)i.. determine the local and convective accelerations when x=3 and t=1.