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1. (10 pts) For the system below, write the 4th modal equation f(t) Base Fixed x,o (t) Assume: に...
1. (20 pts) An LTCI system is defined by the equation *0) + 1) + 4y0)...
1. (20 pts) An LTCI system is defined by the equation *0) + 1) + 4y0) = 10) (a) find the characteristic polynomial, characteristic function equation, characteristic root and characteristic modes of this system. (b) Find yo(t), the zero-input component of the responses y(t) for t > 0 with initial conditions yo(0) = 2 and y(0) = -1. 2. (20 pts) Repeat the previous problem if Vt) + 9y(t) = 351) + 2FE) and yo(0) = 0, Y%(0) = 6.
just simple answers and equations for 3 and 4th problems to solve in Mathcad Vibrations and Acustics Name, SurnameStudent ID Computer NR Nr. -4 System with moving base, Differential equation. Degr...
just simple answers and equations for 3 and 4th problems to
solve in Mathcad
Vibrations and Acustics Name, SurnameStudent ID Computer NR Nr. -4 System with moving base, Differential equation. Degree of Freedom. 3. 1. 2. Establish motion differential equation and obtain displacement and velocity graphs in time for all objects. Use Force balance method! Gravity force, friction force and air resistance is active. Air temperature is 20C9. Cube edge size a-0.05m. Motion possible only in x direction. Given: m-lkg,...
Ae-kt sin út or f(t)-Ae-kt oos ωt des crites the position (10 pts) An equation of the form f(t) of an object in dam...
Ae-kt sin út or f(t)-Ae-kt oos ωt des crites the position (10 pts) An equation of the form f(t) of an object in damped harmonic motion, with the following characteristics: A is the initial amplitude k is the damping constant -is the period The frequency of the motion is simply the reciprocal of the period, ie, fA common unit for frequency is 2e the hertz (Hz), which represents one cycle per second. Suppose the G-string on a violin is plucked...
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, ) luWith u(t, 0) u(t,1)-0...
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, ) luWith u(t, 0) u(t,1)-0 for t>0 (boundary conditions) u(o,z)-3 sin(2x)-5 sin(5z) + sin(6z), for O < < 1 (initial conditions) (20 points)
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, )...
Question 1: The separated solutions of the o fom u(x.t) -X(x)T(t), with the following solutions: ne-dimensional he...
Question 1: The separated solutions of the o fom u(x.t) -X(x)T(t), with the following solutions: ne-dimensional heat equation dtt lu solutions of are - X(x)-Ax +B and T(t) E X(x) = A cos kx + B sin kx and T(t)=Ee-Det The boundary conditions for a metal rod insulated from both sides arex aum = 0 when x =0, and dx (e) Using the boundary conditions for u(x.t) wrie the boundary conditions for XCx), explain for full marks. (b) Find the...
(4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on the (b) Compute the solution u(t, z) for the partial differential equation on the interval [0, T): 16ut = uzz with...
(4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on the (b) Compute the solution u(t, z) for the partial differential equation on the interval [0, T): 16ut = uzz with u(t, 0)-u(t, 1) 0 for t>0 (boundary conditions) (0,) 3 sin(2a) 5 sin(5x) +sin(6x). for 0 K <1 (initial conditions) (20 points) Remember to show your work. Good luck.
(4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on...
only f and g please 1. The motion of a vibrating string of length T, with fixed endpoints, immersed in a fluid (suc...
only f and g please
1. The motion of a vibrating string of length T, with fixed endpoints, immersed in a fluid (such as air) can be modeled by Fu 2&u 21 0rT t>0 at Ot2 (P1) u(0,t)u, t) 0 t20 Qu is a damping term, modelling the effect of at where c,>0. The term proportional to air resistance on the string. (a) Explain why the damping term has a minus sign (2 points) (4 points) (b) Consider the separable...
Olt) 1422LLA 1. The system at the right is subject to the harmonic + x(t) force...
Olt) 1422LLA 1. The system at the right is subject to the harmonic + x(t) force f(t) = Fo sin ot as shown, with amplitude 50 N and a forcing frequency due to a motor (not m shown) with speed = 191 rotations per minute (RPM). Mass m can only translate horizontally and the rod is pinned at point O. The parameters are: r = 5 cm, m= 10 kg, Jo = 1 kg m-, kı = 1000 N/m, ka...
1. (2 pts each) The graph of some unknown function f is given below. 10 6/ 8-64-2 624 10 12 Use the graph to estimate the following quantities: (0 f (9) (g) f(4) b) lim (a) lim (e) (d) lim ( 6)...
1. (2 pts each) The graph of some unknown function f is given below. 10 6/ 8-64-2 624 10 12 Use the graph to estimate the following quantities: (0 f (9) (g) f(4) b) lim (a) lim (e) (d) lim ( 6) (e) lim f(x) (c) lim f(x) if g(x)f(x) 6) a value of r where f is continuous but not differentiable (k) a value of r where f"(x) 0 and f"(x)>0 (1) the location of a relative maximum value...
4. A volume of 30.0 mL of 0.10 M NH, (aq) is titrated with 0.20MCThe value of the base-dissociation (aq) constant, K, for HCO2 in water is 1.2 x 1010 at 25°C. a. (1 pt.) Write the ionic equation...
4. A volume of 30.0 mL of 0.10 M NH, (aq) is titrated with 0.20MCThe value of the base-dissociation (aq) constant, K, for HCO2 in water is 1.2 x 1010 at 25°C. a. (1 pt.) Write the ionic equation for the reaction of NH, (aq) with HCL(aq) (1 pt.) What is the volume of base added at the equivalence point? Show work or reasoning. b. (1 pt.) Will the pH of the equivalence point be higher than, lower than or...
1. (20 pts) An LTCI system is defined by the equation *0) + 1) + 4y0) = 10) (a) find the characteristic polynomial, characteristic function equation, characteristic root and characteristic modes of this system. (b) Find yo(t), the zero-input component of the responses y(t) for t > 0 with initial conditions yo(0) = 2 and y(0) = -1. 2. (20 pts) Repeat the previous problem if Vt) + 9y(t) = 351) + 2FE) and yo(0) = 0, Y%(0) = 6.
just simple answers and equations for 3 and 4th problems to
solve in Mathcad
Vibrations and Acustics Name, SurnameStudent ID Computer NR Nr. -4 System with moving base, Differential equation. Degree of Freedom. 3. 1. 2. Establish motion differential equation and obtain displacement and velocity graphs in time for all objects. Use Force balance method! Gravity force, friction force and air resistance is active. Air temperature is 20C9. Cube edge size a-0.05m. Motion possible only in x direction. Given: m-lkg,...
Ae-kt sin út or f(t)-Ae-kt oos ωt des crites the position (10 pts) An equation of the form f(t) of an object in damped harmonic motion, with the following characteristics: A is the initial amplitude k is the damping constant -is the period The frequency of the motion is simply the reciprocal of the period, ie, fA common unit for frequency is 2e the hertz (Hz), which represents one cycle per second. Suppose the G-string on a violin is plucked...
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, ) luWith u(t, 0) u(t,1)-0 for t>0 (boundary conditions) u(o,z)-3 sin(2x)-5 sin(5z) + sin(6z), for O < < 1 (initial conditions) (20 points)
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, )...
Question 1: The separated solutions of the o fom u(x.t) -X(x)T(t), with the following solutions: ne-dimensional heat equation dtt lu solutions of are - X(x)-Ax +B and T(t) E X(x) = A cos kx + B sin kx and T(t)=Ee-Det The boundary conditions for a metal rod insulated from both sides arex aum = 0 when x =0, and dx (e) Using the boundary conditions for u(x.t) wrie the boundary conditions for XCx), explain for full marks. (b) Find the...
(4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on the (b) Compute the solution u(t, z) for the partial differential equation on the interval [0, T): 16ut = uzz with u(t, 0)-u(t, 1) 0 for t>0 (boundary conditions) (0,) 3 sin(2a) 5 sin(5x) +sin(6x). for 0 K <1 (initial conditions) (20 points) Remember to show your work. Good luck.
(4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on...
only f and g please
1. The motion of a vibrating string of length T, with fixed endpoints, immersed in a fluid (such as air) can be modeled by Fu 2&u 21 0rT t>0 at Ot2 (P1) u(0,t)u, t) 0 t20 Qu is a damping term, modelling the effect of at where c,>0. The term proportional to air resistance on the string. (a) Explain why the damping term has a minus sign (2 points) (4 points) (b) Consider the separable...
Olt) 1422LLA 1. The system at the right is subject to the harmonic + x(t) force f(t) = Fo sin ot as shown, with amplitude 50 N and a forcing frequency due to a motor (not m shown) with speed = 191 rotations per minute (RPM). Mass m can only translate horizontally and the rod is pinned at point O. The parameters are: r = 5 cm, m= 10 kg, Jo = 1 kg m-, kı = 1000 N/m, ka...
1. (2 pts each) The graph of some unknown function f is given below. 10 6/ 8-64-2 624 10 12 Use the graph to estimate the following quantities: (0 f (9) (g) f(4) b) lim (a) lim (e) (d) lim ( 6) (e) lim f(x) (c) lim f(x) if g(x)f(x) 6) a value of r where f is continuous but not differentiable (k) a value of r where f"(x) 0 and f"(x)>0 (1) the location of a relative maximum value...
4. A volume of 30.0 mL of 0.10 M NH, (aq) is titrated with 0.20MCThe value of the base-dissociation (aq) constant, K, for HCO2 in water is 1.2 x 1010 at 25°C. a. (1 pt.) Write the ionic equation for the reaction of NH, (aq) with HCL(aq) (1 pt.) What is the volume of base added at the equivalence point? Show work or reasoning. b. (1 pt.) Will the pH of the equivalence point be higher than, lower than or...
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