1 s+a s+b → The block diagram above shows two transfer functions cascaded in series. The transfer function II(s) of the combined system is known as a lag compensator in controls system design if a < b. Suppose a 100 and b = 10,000. (a) Give the frequency response function G(w) = II (jw) (b) Please describe its asymptotic behavior (the value if constant, or the slope) for the following three regimes: i. low-frequency w b. (c) Sketch the Bode magnitude and phase plots, using decibels as the unit of magnitude and degrees as the unit of phase (d) Suppose the system is driven by a sinusoid. i. If the sinusoid's frequency is 10 Hz, is it amplified, attenuated, or approximately the same? ii. If the sinusoid's frequency is 500 Hz, is it amplified, attenuated, or approximately the same?

A new type of energy absorber is being designed as a buffer at the end of track at a fairground.It consists of a piston with small holes that moves in a cylinder containing oil, so that the kineticenergy of impact is absorbed as heat by the oil.a) Draw a sketch for the instant of impact by a vehicle of mass 2500kg moving at 30mphshowing the forces and energy transfers involved.b) Write down the first law of thermodynamics for a system and identify terms that are notrelevant if the oil is taken as the system.c) How much heat transfer to the surroundings is required to return the oil to its originaltemperature after an impact by a 2500kg vehicle moving at 30mph?

4.) Please help with equation, gravity is g=32.2 ft/sec^2 or g=9.81 m/sec^2

Hang a mass from a spring. We are interested in the moment where you pull the mass down (before you release it) to the highest point that the mass moves to. We also care about when the mass is moving its fastest. In this case, the best place to put the zero reference is where the mass is hanging before you pull on it. 1)Draw an LOL Diagram 2)What is the energy model equation? 3)Will energy be conserved? (i.e., does ΔEsys =0?)