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The system shown below is made up of one mass and two inertia's (M, I1, and...
ME 351: Problem Set 2: Mechanical Systems For the systems shown below: a. Find the free...
ME 351: Problem Set 2: Mechanical Systems For the systems shown below: a. Find the free body diagram showing all forces (including the initial spring forces). Also label the b. positive direction of all displacements and rotations on the free body diagram. Find the governing differential equation (including the initial spring forces). Express the differential equation in standard form (Output and its derivatives in descending order on the left hand side of the equation, Input and its derivatives in descending...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spr...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
Please show work 3. Given a mass-spring-damper system, the 2kg mass is connected to two linear...
Please show work
3. Given a mass-spring-damper system, the 2kg mass is connected to two linear springs with stiffness coefficients ki- 100 N/m and ki 150 N/m and a viscous damper with b 50 Ns/m. A constant force of SN is applied as shown. The effect of friction is negligible. ki m b 3.1 [2pts] Determine the equivalent stiffness of the springs. 3.2 [3pts] Draw the free-body diagram of the system. Define the generalized coordinate and label your forces and...
Consider a mass-spring-damper system whose motion is described by the following system of differe...
Consider a mass-spring-damper system whose motion is described by the following system of differentiat equations [c1(f-k)+k,(f-х)-c2(x-9), f=f(t), y:' y(t) with x=x( t), where the function fit) is the input displacement function (known), while xit) and yt) are the two generalized coordinates (both unknown) of the mass-spring-damper systenm. 1. Identify the type of equations (e.g. H/NH, ODE/PDE, L/NL, order, type of coefficients, etc.J. 2. Express this system of differential equations in matrix form, assume f 0 and then determine its general...
Electro-Mechanical Systems The electro-mechanical system shown below consists of an electric motor with input voltage V,...
Electro-Mechanical Systems The electro-mechanical system shown below consists of an electric motor with input voltage V, which drive inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System L > Vbac Voac Motor I - Motor Input Voltage Vpac - Motor Back EMF = Kas 0 0 - Motor Angular Velocity I - Motor Output...
Problem 1: The system in Figure 1 comprises two masses connected to one another through a...
Problem 1: The system in Figure 1 comprises two masses connected to one another through a spring. The block slides without friction on the support and has mass mi. The disk has radius a, mass moment of inertia I, and mass m2. The disk rolls without slipping on the support. The springs are unstretched when x(t) = x2(t) = 0. 2k 3k , m Figure 1: System for Problem 1 (a) Derive the differential equations of motion for the system...
The equations of motion for a mass-spring-damper system can be described by mE(t) + ci(t) +...
The equations of motion for a mass-spring-damper system can be described by mE(t) + ci(t) + k2(t) = F(t), where z(t) is the position of the mass, c is the damper coefficient, k is the spring constant, and F(t) is an external force applied to the mass as an input. If the system state vector is defined by 2(t) = lat) a(t)=F(t), y(t)=2(t), given below: x=Ax + Bu y=Cx + Du.
. The system shown below consists of a homogeneous rigid rod with mass m, length l,...
. The system shown below consists of a homogeneous rigid rod with mass m, length l, and mass center of gravity G where the mass moment of inertia of the rod about G is given by: Translational spring with stiffness k supports the rod at point B, and rotational damper c, İs connected to the rod at its pivot point A as shown.ft) is an external force applied to the rod. Derive the equation of motion of the single degree...
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from...
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from springs with constants k, and ky, respectively. Assuming that there is no damping in the system, the displacement y(t) of the bottom mass m, from its equilibrium positions satisfies the 4-order equation (4) y2 + k + k)y + k_k2yz = e-2, where f(t) = e-2 is an outside force driving the motion of m. If a 24 N weight would stretch the top...
4. Given the mechanical system shown in the following diagram: 6,,02 J, K, No slip-_ F(t) Massles...
4. Given the mechanical system shown in the following diagram: 6,,02 J, K, No slip-_ F(t) Massless rack a. Draw the FBD for each inertia and for the rack: Develop the basic equations of motion for each of the three mass elements (do it for the rack, even though its inertia is zero). Do not solve for spring and damper b. forces yet: leave answers in terms of jki, ma.,jai,fo, etc. What is the "stretch" in the spring K2 and...
ME 351: Problem Set 2: Mechanical Systems For the systems shown below: a. Find the free body diagram showing all forces (including the initial spring forces). Also label the b. positive direction of all displacements and rotations on the free body diagram. Find the governing differential equation (including the initial spring forces). Express the differential equation in standard form (Output and its derivatives in descending order on the left hand side of the equation, Input and its derivatives in descending...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
Please show work
3. Given a mass-spring-damper system, the 2kg mass is connected to two linear springs with stiffness coefficients ki- 100 N/m and ki 150 N/m and a viscous damper with b 50 Ns/m. A constant force of SN is applied as shown. The effect of friction is negligible. ki m b 3.1 [2pts] Determine the equivalent stiffness of the springs. 3.2 [3pts] Draw the free-body diagram of the system. Define the generalized coordinate and label your forces and...
Consider a mass-spring-damper system whose motion is described by the following system of differentiat equations [c1(f-k)+k,(f-х)-c2(x-9), f=f(t), y:' y(t) with x=x( t), where the function fit) is the input displacement function (known), while xit) and yt) are the two generalized coordinates (both unknown) of the mass-spring-damper systenm. 1. Identify the type of equations (e.g. H/NH, ODE/PDE, L/NL, order, type of coefficients, etc.J. 2. Express this system of differential equations in matrix form, assume f 0 and then determine its general...
Electro-Mechanical Systems The electro-mechanical system shown below consists of an electric motor with input voltage V, which drive inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System L > Vbac Voac Motor I - Motor Input Voltage Vpac - Motor Back EMF = Kas 0 0 - Motor Angular Velocity I - Motor Output...
Problem 1: The system in Figure 1 comprises two masses connected to one another through a spring. The block slides without friction on the support and has mass mi. The disk has radius a, mass moment of inertia I, and mass m2. The disk rolls without slipping on the support. The springs are unstretched when x(t) = x2(t) = 0. 2k 3k , m Figure 1: System for Problem 1 (a) Derive the differential equations of motion for the system...
The equations of motion for a mass-spring-damper system can be described by mE(t) + ci(t) + k2(t) = F(t), where z(t) is the position of the mass, c is the damper coefficient, k is the spring constant, and F(t) is an external force applied to the mass as an input. If the system state vector is defined by 2(t) = lat) a(t)=F(t), y(t)=2(t), given below: x=Ax + Bu y=Cx + Du.
. The system shown below consists of a homogeneous rigid rod with mass m, length l, and mass center of gravity G where the mass moment of inertia of the rod about G is given by: Translational spring with stiffness k supports the rod at point B, and rotational damper c, İs connected to the rod at its pivot point A as shown.ft) is an external force applied to the rod. Derive the equation of motion of the single degree...
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from springs with constants k, and ky, respectively. Assuming that there is no damping in the system, the displacement y(t) of the bottom mass m, from its equilibrium positions satisfies the 4-order equation (4) y2 + k + k)y + k_k2yz = e-2, where f(t) = e-2 is an outside force driving the motion of m. If a 24 N weight would stretch the top...
4. Given the mechanical system shown in the following diagram: 6,,02 J, K, No slip-_ F(t) Massless rack a. Draw the FBD for each inertia and for the rack: Develop the basic equations of motion for each of the three mass elements (do it for the rack, even though its inertia is zero). Do not solve for spring and damper b. forces yet: leave answers in terms of jki, ma.,jai,fo, etc. What is the "stretch" in the spring K2 and...
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