Design a proportional controller (i.e. find K) for the shown system in order to have a damping ratio: zeta=0.4 U(s) Y(s) 1 s? + 2s + 4 K Select one: O a. 2.25 O b. 1.0 O c. 2.0 O d. 8.25 e. 4.25
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- A block of mass 0.688 kilograms resting on a smooth horizontal surface is attached to a spring with a spring constant of 33.4 newtons per meter. The block is pulled horizontally 14.1 centimeters from its equilibrium position and released. a. What is the total mechanical energy of the system? Include units in your answer. b. What is the speed of the block when it is 9.0 centimeters from its equilibrium position? Include units in your answer. c. One end of the spring is then attached to a support so it hangs vertically, and the block is suspended from it and lowered into a resting position. How far does the block stretch the spring? Include units in your answer. d. As shown below, the block is then lifted 14.1 centimeters (labeled d in the figure) and released. What is the speed of the block when it is 9.0 centimeters from its equilibrium position (labeled y in the figure)? Include units in your answer. More information. Hint: Since the vertical position of the block is changing,…Two identical springs are connected in series as shown, each spring has a spring constant of 30 N/m. What is the spring constant of the overall two-spring system, in N/m? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.A spring with a spring constant of k=157N/m is initially compressed by a block a distance d=0.21m. The block is on horizontal surface with coefficient of kinetic friction yk static friction ys and has a mass of m=6kg B)Assuming the block is released from the initial position and begins to move to the right input an expression for the sum of the force in the x- direction in the configuration.
- 13A block of mass 0.688 kilograms resting on a smooth horizontal surface is attached to a spring with a spring constant of 33.4 newtons per meter. The block is pulled horizontally 14.1 centimeters from its equilibrium position and released. a. What is the total mechanical energy of the system? Include units in your answer. b. What is the speed of the block when it is 9.0 centimeters from its equilibrium position? Include units in your answer. c. One end of the spring is then attached to a support so it hangs vertically, and the block is suspended from it and lowered into a resting position. How far does the block stretch the spring? Include units in your answer. d. As shown below, the block is then lifted 14.1 centimeters (labeled d in the figure) and released. What is the speed of the block when it is 9.0 centimeters from its equilibrium position (labeled y in the figure)? Include units in your answer. More information. Hint: Since the vertical position of the block is changing,…A 0.41-kg metal sphere oscillates at the end of a vertical spring. As the spring stretches from 0.12 m to 0.23 m (relative to its unstrained length), the speed of the sphere decreases from 7.0 to 4.5 m/s. What is the spring constant of the spring? Number i 306.17 Units N/n