Please create a MATLAB function named "fall_error" that takes as input (1) a time step for free fall in seconds and (2) the time of fall in seconds (in that order) and returns the error (in meters) that occurs when comparing the z discretization from lecture to the analytical solution from calculus. Write a script which calls the above function and creates a color map with one axis as the time step (in seconds) and one axis as the time of fall (in number of steps) and the color axis representing the error (in m). Please make this map at least 5x5 and add a short commentary on why your map makes sense (seems correct).

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?

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.

Which from the following instrument is commonly used to detect the high pitch butzing sound in bearings? [clo4] a)-digital ultrasonic meter b)-infrared camera c)-spectroscopic d)-vibrometer