The root-mean-square (RMS) value of a periodic function x(t) is given by rms = √ 1 T ∫ x2() T 0 , with T being the period. Use this equation to show that the RMS value of a sinusoidal wave () = m cos( + theta) V is rms = m √2 ⁄ . You may need the trigonometric identity cos2 theta = 1 2 (cos2theta + 1).

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.

Fluids at rest possess no flow energy. a)- true b)- false

Determine whether or not it is possible to compress air adiabatically from k to 140 kpa and 400 k. what is the entropy change during this process?