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Problem 2 (25%). Deriving the EOM and finding the response. The inverted pendulum below consists of...
Question 1.0 [25 marks] Consider the sketch below which an inverted pendulum. bob, M Damper,c spring,k...
Question 1.0 [25 marks] Consider the sketch below which an inverted pendulum. bob, M Damper,c spring,k connecting rod mass, m に., pivot Fig 1.0 Determine: i. equivalent inertia ii. equivalent stiffness equivalent damping properties for the system. Derive the natural frequency of the system
Problem 2: The inverted pendulum, illustrated in Figure 1, is one of the most studied models...
Problem 2: The inverted pendulum, illustrated in Figure 1, is one of the most studied models in dynamic and control courses given its simplicity despite its complex nonlinear behavior. It can be used to model tall buildings under seismic and wind motion, moving rockets, and satellites. The linearized (ie., approximated) equation of motion is given by: mg ml?.(t)- mgl.0(t) = T(t) where m, L, and g are constants representing the mass, length, and gravity: o denotes the angular position of...
Problem 6 State space representation of motor - driven cart with inverted pendulum You are given...
Problem 6 State space representation of motor - driven cart with inverted pendulum You are given that the cart carrying the inverted pendulum shown in the figure below is driven by an electric motor powering one pair of wheels so that the whole cart, pendulum and all, becomes the load on the motor. z is the cart position, M is its mass, θ is the pendulum angle with respect to the vertical, I its length, and m its mass. The...
Problem 3 (70 pts): Consider the mechanical system in Figure , the so-called "cart pendulum" system....
Problem 3 (70 pts): Consider the mechanical system in Figure , the so-called "cart pendulum" system. The cart has a moving mass M, and is connected to a linear motor via a flexible coupling with stiffness K and damping B. An inverted pendulum of length1, negligible inertia and mass m is attached to the cart via a rotary actuator. If the pendulum damping coefficient is b, the linear actuator force is F and the rotary actuator torque is t 1)...
Problem Statement: A clock pendulum (shown below) is idealized as a circular disk, of ass m and r...
Ideal clock pendulum(treat as a rigid body)
Problem Statement: A clock pendulum (shown below) is idealized as a circular disk, of ass m and radius R, attached at the end of a rigid, massless rod having length L . D raw a complete Free Body Diagram, treating the whole pendulum as a rigid body. Using the indicated coordinate axes, basis vectors, and system parameters, determine the items below a) The vector form of the Force Balance Law (FBL). (Make sure...
PROBLEM 2.In the sketch a three part physical pendulum is shown, consisting of two massless rods...
PROBLEM 2.In the sketch a three part physical pendulum is shown, consisting of two massless rods (L=1 m) which make a 90 angle with respect to each other and are constrained to pivot at about an axis that is perpendicular to the paper and at the corner of where they meet. Two unequal point masses aresolidly attached, one at each end. The rod oscillates (when disturbed from equilibrium) due to the downward force of gravity. (ignore friction and air resistance)....
Problem 4: Read Appendix 2 below (Sec. 1.4.1 of Kasap) and then solve. A metallic back...
Problem 4: Read Appendix 2 below (Sec. 1.4.1 of Kasap) and then solve. A metallic back contact is applied to the CdTe solar cell of Problem 1 using a set up similar to that described in Figure 1.74 (b) on the next page. To form the metallic back contact, two evaporation sources are used, Cu and Au. An initial 3 nm layer of Cu is deposited first and then 30 nm of Au is deposited. After these depositions, the sample...
Question 1.0 [25 marks] Consider the sketch below which an inverted pendulum. bob, M Damper,c spring,k connecting rod mass, m に., pivot Fig 1.0 Determine: i. equivalent inertia ii. equivalent stiffness equivalent damping properties for the system. Derive the natural frequency of the system
Problem 2: The inverted pendulum, illustrated in Figure 1, is one of the most studied models in dynamic and control courses given its simplicity despite its complex nonlinear behavior. It can be used to model tall buildings under seismic and wind motion, moving rockets, and satellites. The linearized (ie., approximated) equation of motion is given by: mg ml?.(t)- mgl.0(t) = T(t) where m, L, and g are constants representing the mass, length, and gravity: o denotes the angular position of...
Problem 6 State space representation of motor - driven cart with inverted pendulum You are given that the cart carrying the inverted pendulum shown in the figure below is driven by an electric motor powering one pair of wheels so that the whole cart, pendulum and all, becomes the load on the motor. z is the cart position, M is its mass, θ is the pendulum angle with respect to the vertical, I its length, and m its mass. The...
Problem 3 (70 pts): Consider the mechanical system in Figure , the so-called "cart pendulum" system. The cart has a moving mass M, and is connected to a linear motor via a flexible coupling with stiffness K and damping B. An inverted pendulum of length1, negligible inertia and mass m is attached to the cart via a rotary actuator. If the pendulum damping coefficient is b, the linear actuator force is F and the rotary actuator torque is t 1)...
Ideal clock pendulum(treat as a rigid body)
Problem Statement: A clock pendulum (shown below) is idealized as a circular disk, of ass m and radius R, attached at the end of a rigid, massless rod having length L . D raw a complete Free Body Diagram, treating the whole pendulum as a rigid body. Using the indicated coordinate axes, basis vectors, and system parameters, determine the items below a) The vector form of the Force Balance Law (FBL). (Make sure...
Problem 4: Read Appendix 2 below (Sec. 1.4.1 of Kasap) and then solve. A metallic back contact is applied to the CdTe solar cell of Problem 1 using a set up similar to that described in Figure 1.74 (b) on the next page. To form the metallic back contact, two evaporation sources are used, Cu and Au. An initial 3 nm layer of Cu is deposited first and then 30 nm of Au is deposited. After these depositions, the sample...
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