Find expressions for pressure as a function of density and density in terms of pressure of an isentropic ideal gas

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

An air conditioning system consist of a 5 cm diameter pipe, operating at a pressure of 200 kpa. the air initially enters the pipe at 15°c with a velocity of 20 m/s and relative humidity of 80%. if the heat supply throughout the process is 960 w, determine the relative humidity and the temperature at the outlet

An electric motor is used to drive a power press which makes steel turning moment diagrams 323 pressings from a metal sheet. the motor runs at a mean speed of 50 rev/s. the torque required is 10.0nm for 0.2s, followed by 1.0nm for0.3 s with this sequence then being repeated. what is the minimum power required of the motor and the moment of incrtia required for the t1ywhcel if the speed fluctuations are to be restricted to 1.5%?