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Problem 5. Consider the dynamics of two mass mechanical system captured by d2xi(t) Middt?t2+k(x1(t)-x2(t)) = f(t)...
x2(t) m2 2 Two masses, m1 and m2, are connected with a spring, k. A force,...
x2(t) m2 2 Two masses, m1 and m2, are connected with a spring, k. A force, f (t), is applied on the first mass. Both masses experience viscous damping, c1 and c2, through the surface that they sit on. The equations of motion that describe the system dynamics are m2 (t)--CzX2 (t)-k(X2(t)-x,(t)) The initial conditions are: x1(0) - a x(0)b (0) = c Assuming zero initial conditions, rearrange the two equations of motion to find the response for X1(s) and...
please help. Note: u(t) is unit-step function Consider the system with the differential equation: dyt) +...
please help.
Note: u(t) is unit-step function Consider the system with the differential equation: dyt) + 2 dy(t) + 2y(t) = dr(t) – r(e) dt2 dt where r(t) is input and y(t) is output. 1. Find the transfer function of the system. Note that transfer function is Laplace transform ratio of input and output under the assumption that all initial conditions are zero. 2. Find the impulse response of the system. 3. Find the unit step response of the system...
the following problem is of a two-mass system. I have 2 questions 1. find the transfer...
the following problem is of a two-mass system. I have 2
questions
1. find the transfer function from input F2 to output x1
2. for the transfer function found, determine the sensitivity to
variation in parameter B12
note: i already found the differential eqns of motion for
t>0
Problem formulation Two masses are connected as shown in Fig. 1. Input forces Fi(t) and F.(t) act on masses m, and mg, respectively. The outputs are positions xi(t) and x2(t). Initial conditions...
w a. Obtain the transfer functions X1(s)/U(s) and X2(s)/U(s) of the mechanical system shown in the...
w a. Obtain the transfer functions X1(s)/U(s) and X2(s)/U(s) of the mechanical system shown in the figure. b. Solve the transfer function to retrieve the information on the response function (as a function of time t) by assuming the m1 = m2 and ki = ki =k3 C. Plot the response function d. Show the impact of doubling the mass m2 = 2m1 on the response function - plot it to compare it with that described in case C
Consider the following problem min f(x)=x1+x2 T2 Suppose that the logarithmic barrier method is used to...
Consider the following problem min f(x)=x1+x2 T2 Suppose that the logarithmic barrier method is used to solve this problem. (a) What is 1k(ek)? Find x* assuming {rk}-> 1", įfek-> 0 when k-oo. (b) Compute the Hessian matrix H of the augmented objective function f(x) - f(x)*(x), where B(x) is the logarithmic barrier function, setting e* to 104 What is the condition number of H? What is H-1?
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical system subjected to fluctuations (t) at the wall is provided in figure 2. Spring k, is interconnected with both spring ka and damper Os at the nodal point. The independent displacement of mass m is denoted by 1, the independent displacement of mass m, is denoted by r2, and the independent displacement of the node is denoted by ra. Assume a linear force-displacement/velocity relationship...
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...
Question 3 a) Develop the transfer function X2%)/F(s) of the mechanical system shown in Figure 3(a)....
Question 3 a) Develop the transfer function X2%)/F(s) of the mechanical system shown in Figure 3(a). Give and explain one example the real application where you can relate with this system (5 marks) b) Routh's stability criterion is of limited usefulness in linear control systems analysis mainly because it does not suggest how to stabilize an unstable system. Thus, we should evaluate the stability range of a parameter value. Consider the servo system with tachometer feedback as shown in Figure...
For a mass-spring-damper mechanical systems shown below, x200) K1-1 N/m 0000 -X,(0) K-1 N/m 00004 =...
For a mass-spring-damper mechanical systems shown below, x200) K1-1 N/m 0000 -X,(0) K-1 N/m 00004 = 1 N-s/m fr2 M1=1 kg = 2 N-s/m M2 -1 kg 13 = 1 N-s/m 1. Find the differential equations relating input force f(t) and output displacement xi(t) and x2(C) in the system. (40 marks) (Hint: K, fy and M are spring constant, friction coefficient and mass respectively) 2. Determine the transfer function G(s)= X1(s)/F(s) (20 marks)
... Metro by T-Mobile 11:02 PM X MECH_371_Proble... E .. MECH 371 Spring 2020: Problem Set...
... Metro by T-Mobile 11:02 PM X MECH_371_Proble... E .. MECH 371 Spring 2020: Problem Set 3 (/ ) of the systems assuming zero initial conditions 1. Determine the transfer function described by (0)+(1) = 3x(1)+i(1) 2. Consider the system H(S)=7+45+3 (a) Calculate the poles anders of the system (b) Calculate the wep response 3. Determine the transfer function V_ (Assuming zero initial conditions _(s) for the following electrical circuit systems iO +40 4. Consider the system MW f(t) :...
x2(t) m2 2 Two masses, m1 and m2, are connected with a spring, k. A force, f (t), is applied on the first mass. Both masses experience viscous damping, c1 and c2, through the surface that they sit on. The equations of motion that describe the system dynamics are m2 (t)--CzX2 (t)-k(X2(t)-x,(t)) The initial conditions are: x1(0) - a x(0)b (0) = c Assuming zero initial conditions, rearrange the two equations of motion to find the response for X1(s) and...
please help.
Note: u(t) is unit-step function Consider the system with the differential equation: dyt) + 2 dy(t) + 2y(t) = dr(t) – r(e) dt2 dt where r(t) is input and y(t) is output. 1. Find the transfer function of the system. Note that transfer function is Laplace transform ratio of input and output under the assumption that all initial conditions are zero. 2. Find the impulse response of the system. 3. Find the unit step response of the system...
the following problem is of a two-mass system. I have 2
questions
1. find the transfer function from input F2 to output x1
2. for the transfer function found, determine the sensitivity to
variation in parameter B12
note: i already found the differential eqns of motion for
t>0
Problem formulation Two masses are connected as shown in Fig. 1. Input forces Fi(t) and F.(t) act on masses m, and mg, respectively. The outputs are positions xi(t) and x2(t). Initial conditions...
w a. Obtain the transfer functions X1(s)/U(s) and X2(s)/U(s) of the mechanical system shown in the figure. b. Solve the transfer function to retrieve the information on the response function (as a function of time t) by assuming the m1 = m2 and ki = ki =k3 C. Plot the response function d. Show the impact of doubling the mass m2 = 2m1 on the response function - plot it to compare it with that described in case C
Consider the following problem min f(x)=x1+x2 T2 Suppose that the logarithmic barrier method is used to solve this problem. (a) What is 1k(ek)? Find x* assuming {rk}-> 1", įfek-> 0 when k-oo. (b) Compute the Hessian matrix H of the augmented objective function f(x) - f(x)*(x), where B(x) is the logarithmic barrier function, setting e* to 104 What is the condition number of H? What is H-1?
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical system subjected to fluctuations (t) at the wall is provided in figure 2. Spring k, is interconnected with both spring ka and damper Os at the nodal point. The independent displacement of mass m is denoted by 1, the independent displacement of mass m, is denoted by r2, and the independent displacement of the node is denoted by ra. Assume a linear force-displacement/velocity relationship...
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...
Question 3 a) Develop the transfer function X2%)/F(s) of the mechanical system shown in Figure 3(a). Give and explain one example the real application where you can relate with this system (5 marks) b) Routh's stability criterion is of limited usefulness in linear control systems analysis mainly because it does not suggest how to stabilize an unstable system. Thus, we should evaluate the stability range of a parameter value. Consider the servo system with tachometer feedback as shown in Figure...
For a mass-spring-damper mechanical systems shown below, x200) K1-1 N/m 0000 -X,(0) K-1 N/m 00004 = 1 N-s/m fr2 M1=1 kg = 2 N-s/m M2 -1 kg 13 = 1 N-s/m 1. Find the differential equations relating input force f(t) and output displacement xi(t) and x2(C) in the system. (40 marks) (Hint: K, fy and M are spring constant, friction coefficient and mass respectively) 2. Determine the transfer function G(s)= X1(s)/F(s) (20 marks)
... Metro by T-Mobile 11:02 PM X MECH_371_Proble... E .. MECH 371 Spring 2020: Problem Set 3 (/ ) of the systems assuming zero initial conditions 1. Determine the transfer function described by (0)+(1) = 3x(1)+i(1) 2. Consider the system H(S)=7+45+3 (a) Calculate the poles anders of the system (b) Calculate the wep response 3. Determine the transfer function V_ (Assuming zero initial conditions _(s) for the following electrical circuit systems iO +40 4. Consider the system MW f(t) :...
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