Modeling horizontal pendulum. Derive a differential equation relating the input, torque T,with the output, angular displacement θ. Damping coefficient is D. Moment of inertia of pendulum is 1/3mL2
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Modeling horizontal pendulum. Derive a differential equation
relating the input, torque T,with the output, angular
displacement...
3) For the system shown in the figure, the input is the torque T(t) and the...
3) For the system shown in the figure, the input is the torque T(t) and the outputs are the linear displacements x(t) and the angular displacement θ(t). The equilibrium position corresponds to x 0 0. Note that there is viscous friction between the rack and the surface it slides on. Also, you may treat the small diameter shaft as massless and rigid. mr Clearly state all assumptions to be used for modeling this system. Draw the freebody diagrams. State your...
s) Given the following rotational mechanical system, hot relates the input variable T (applied torque) to...
s) Given the following rotational mechanical system, hot relates the input variable T (applied torque) to the output a) Write the differential equation that re variable angular displacement) b) Convert the differential equatio c) Write the Transfer function of the system (I. w ent the differential equation to Laplace domain assuming initial conditions Zero Consider the following values for the parameters: J - 2 kg-m? (moment of inertial of the mass) D = 0.5 N-m-s/rad (coefficient of friction) K-1 N-m/rad...
Consider the system given below. The output is y(displacement from equilibrium position) and the input is...
Consider the system given below. The output is y(displacement from equilibrium position) and the input is V. (source voltage). The motor has an electrical constant Ke, a torque constant K, an armature inductance Lg and a resistance R. The rotor, shaft and disk together have inertia J and a viscous friction coefficient B. The disk has a radius ofr. (For the motor, assume that the torque is T = Ki,, and the back EMF is emf = KO). a. Derive...
Find the differential equation relating input x(t) to output y(t) for the following circuit: Please be...
Find the differential equation relating input x(t) to output
y(t) for the following circuit: Please be descriptive, I would like
to understand all parts of the equation better.
x(t) y(il
PARTS: a-c Problem 1 (40 points) The rotational system shown in this diagram has a single...
PARTS: a-c
Problem 1 (40 points) The rotational system shown in this diagram has a single torque input, T(t), and a single angular displacement output, (t). Also shown are the shaft polar moment of inertia, J, torsional spring constant, k, and rotational viscous damping coefficient, c. From the law of rotation (sum of the moments equal to polar moment of inertia times angular acceleration), we obtain: jä(t) + c)(t) + ko(t) = T(t). This ordinary differential equation is second-order, linear...
2. (20 points) A field controlled DC motor model is given below where eaſt) is an...
2. (20 points) A field controlled DC motor model is given below where eaſt) is an applied input voltage, ia(t) is the armature current, Ra and La are the armature resistance and inductance, respectively, e(t) is a back (or counter) emf (electro-motive force) le (t) = K w here K is a motor (torque) constant, t(t) is the torque generated by the motor, w(t) is the angular velocity, 0(t) is the angular position, J represents the rotor inertia and load...
Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input to...
Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input torque is supplied by an electric motor Specifically, T(t) T(t) -Kamp Vin(t) where 1) "Vin is the input voltage supplied to the motor N-m 2) "Kamp" is the motor gain (this constant has units of Volt) So, the transfer function for this system is (s)Kamp The moment of inertia is known...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input x(t) 1. ド ド Ki Derive the transfer function X,G)/X, (s)of the mechanical system shown below. The displacements x, and xo are measured from their respective equilibrium potions. Is the system a first-order system if so, what is the time constant? 2. k1 bz k2 3. Consider the mechanical system shown below. The system is initially at rest. The displacements x, and x2 are...
2. The angular displacement e(t) of a damped forced pendulum of length 1 swinging in a...
2. The angular displacement e(t) of a damped forced pendulum of length 1 swinging in a vertical plane under the influence of gravity can be modelled with the second order non-homogeneous ODE 0"(t) + 270'(t) +w20(t) = f(t), (2) where wa = g/l. The second term in the equation represents the damping force (e.g. air resistance) for the given constant 7 > 0. The model can be used to approximate the motion of a magnetic pendulum bob being driven by...
Prelab Preparation: For the RC circuit shown in Figure 1, derive the modeling equation relating the output volta ge...
Prelab Preparation: For the RC circuit shown in Figure 1, derive the modeling equation relating the output volta ge Vout to the input voltage vin. What is the transfer function? What is the time constant of the system? Vout Figure 1: RC Circuit What is the analytical step response solution in terms of vin, Rand C? For assumed values of R 1 K, and C 6.8 uF, perform a simulation using Matlab/Simulink assuming an input square wave signal of 5Vpp,...
3) For the system shown in the figure, the input is the torque T(t) and the outputs are the linear displacements x(t) and the angular displacement θ(t). The equilibrium position corresponds to x 0 0. Note that there is viscous friction between the rack and the surface it slides on. Also, you may treat the small diameter shaft as massless and rigid. mr Clearly state all assumptions to be used for modeling this system. Draw the freebody diagrams. State your...
s) Given the following rotational mechanical system, hot relates the input variable T (applied torque) to the output a) Write the differential equation that re variable angular displacement) b) Convert the differential equatio c) Write the Transfer function of the system (I. w ent the differential equation to Laplace domain assuming initial conditions Zero Consider the following values for the parameters: J - 2 kg-m? (moment of inertial of the mass) D = 0.5 N-m-s/rad (coefficient of friction) K-1 N-m/rad...
Consider the system given below. The output is y(displacement from equilibrium position) and the input is V. (source voltage). The motor has an electrical constant Ke, a torque constant K, an armature inductance Lg and a resistance R. The rotor, shaft and disk together have inertia J and a viscous friction coefficient B. The disk has a radius ofr. (For the motor, assume that the torque is T = Ki,, and the back EMF is emf = KO). a. Derive...
Find the differential equation relating input x(t) to output
y(t) for the following circuit: Please be descriptive, I would like
to understand all parts of the equation better.
x(t) y(il
PARTS: a-c
Problem 1 (40 points) The rotational system shown in this diagram has a single torque input, T(t), and a single angular displacement output, (t). Also shown are the shaft polar moment of inertia, J, torsional spring constant, k, and rotational viscous damping coefficient, c. From the law of rotation (sum of the moments equal to polar moment of inertia times angular acceleration), we obtain: jä(t) + c)(t) + ko(t) = T(t). This ordinary differential equation is second-order, linear...
2. (20 points) A field controlled DC motor model is given below where eaſt) is an applied input voltage, ia(t) is the armature current, Ra and La are the armature resistance and inductance, respectively, e(t) is a back (or counter) emf (electro-motive force) le (t) = K w here K is a motor (torque) constant, t(t) is the torque generated by the motor, w(t) is the angular velocity, 0(t) is the angular position, J represents the rotor inertia and load...
Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input torque is supplied by an electric motor Specifically, T(t) T(t) -Kamp Vin(t) where 1) "Vin is the input voltage supplied to the motor N-m 2) "Kamp" is the motor gain (this constant has units of Volt) So, the transfer function for this system is (s)Kamp The moment of inertia is known...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input x(t) 1. ド ド Ki Derive the transfer function X,G)/X, (s)of the mechanical system shown below. The displacements x, and xo are measured from their respective equilibrium potions. Is the system a first-order system if so, what is the time constant? 2. k1 bz k2 3. Consider the mechanical system shown below. The system is initially at rest. The displacements x, and x2 are...
2. The angular displacement e(t) of a damped forced pendulum of length 1 swinging in a vertical plane under the influence of gravity can be modelled with the second order non-homogeneous ODE 0"(t) + 270'(t) +w20(t) = f(t), (2) where wa = g/l. The second term in the equation represents the damping force (e.g. air resistance) for the given constant 7 > 0. The model can be used to approximate the motion of a magnetic pendulum bob being driven by...
Prelab Preparation: For the RC circuit shown in Figure 1, derive the modeling equation relating the output volta ge Vout to the input voltage vin. What is the transfer function? What is the time constant of the system? Vout Figure 1: RC Circuit What is the analytical step response solution in terms of vin, Rand C? For assumed values of R 1 K, and C 6.8 uF, perform a simulation using Matlab/Simulink assuming an input square wave signal of 5Vpp,...
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