Assume that a particular temperature probe approximates first-order behavior in a particular application, it has a time constant of 6s, and it is suddenly subjected to a temperature step from an unknown starting point to 400°F. If the termperature indicated after 20 seconds is 387°F, then what was the temperature at the starting point?

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.