Not me staying up till 1 am watching t. i.k t. o.k lol

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.

A-mn has a cubic structure with a0 0.8931 nm and a density of 7.47 g/cm3. b-mn has a different cubic structure, with a0 0.6326 nm and a density of 7.26 g/cm3. the atomic weight of manganese is 54.938 g/mol and the atomic radius is 0.112 nm. determine the percent volume change that would occur if a-mn transforms to b-mn.

Water at the rate of 1 kg/s is forced through a tube with a 2.5 cm inner diameter. the inlet water temperature is 15°c, and the outlet water temperature is 50°c. the tube wall temperature is 14°c higher than the local water temperature all along the length of the tube. what is the length of the tube?