An inverted pendulum on a cart is 53 cm long. The cart suddenly moves by 2.4 mm. Use gravitational acceleration of 9.81 m/s2. (a) We know from the inverted pendulum analysis that using proportional feedback for the pendulum, the system response is oscillatory. If K = 114.3 cm/rad, obtain the response of the pendulum (i. e., et)), its amplitude, and the period of oscillation. (b) Obtain the response function., et), for the same pendulum if we use proportional-plus-integral feedback with K = 114.3 cm/radian and K2 = 668.1 cm/s-radian.

1. what is the relationship between wavelength and the penetrating power of an electromagnetic wave? a) the penetrating power has no relationship to the wavelength. b) the penetrating power increases as the wavelength increases. c) the penetrating power decreases as the wavelength increases. d) the penetrating power decreases as the wavelength decreases. 2. as ice melts and turns into water, the speed of sound through the material would most likely do what? justify your answer. a) the speed would not change because the material is always water. b) the speed of sound would increase because the density of water is less than that of ice. c) the speed of sound would increase because energy is added to ice in order to make it melt. d) the speed of sound would decrease because sound travels faster through solids than liquids. 3.which of these waves need a medium to travel through? a) sound b) x-rays c) infrared rays d) visible light