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3. Given the following system that is harmonically excited by x(t) = Xo sin at. Xosin(ot)...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
7. 150 points) A one-degree-of-freedom system is shown below. (a) (50 points) Derive the differential equation...
7. 150 points) A one-degree-of-freedom system is shown below. (a) (50 points) Derive the differential equation governing the motion of the system usingq, the (b) (25 points) what are the natural frequency and damping ratto of the system? c) (25 points) Mc)-0 (d) (25 points) (e) (25 points) If M(t) =1.2 sin m N clockwise angular displacement of the disk from equilibrium as the generalized coordinate. 10° and the system is given an initial angulan released from rest what is...
1. A two story building is represented in the figure below by a lumped mass systen...
1. A two story building is represented in the figure below by a lumped mass systen in which m1 = m2 and k1 = k2. The ground is given a harmonic motion y Ysin at. Draw the appropriate free body diagrams. (5 points) a. b. Write the equations of motion in matrix form. (5 points) c. Solve for the natural frequencies and mode shapes. (10 points) d. Solve for the displacement amplitude response of xi and x2. (10 points)
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
The motion of a body is described by the equation 4.15 sin (0.170πt) where t is...
The motion of a body is described by the equation 4.15 sin (0.170πt) where t is in s and y is in m. a. Find the amplitude b. Find the period c. Find the frequency d. Find the displacement at t= 5.50 s e. Find the displacement at t= 22.5 s
The motion of a body is described by the equation 1.40 sin (0.130πt) where t is...
The motion of a body is described by the equation 1.40 sin (0.130πt) where t is in s and y is in m. (a) Find the amplitude. (b) Find the period. (c) Find the frequency. (d) Find the displacement at t = 3.50 s. (e) Find the displacement at t = 29.0 s.
418. The e spring k and the dashpot c of the accompanying diagram are fastened together at A; x r...
418. The e spring k and the dashpot c of the accompanying diagram are fastened together at A; x represents the absolute displacement of m, and y is the abso- lute displacement of the point A. The motion o (a) Construct the free-body diagram for m. (b) Write the differential equation of motion for m (c) Obtain the solution for the steady-state motion of m. (d) Determine the relation for the impressed force at A. A is defined by y-...
Problem # 4 15 points The base of a damped spring-mass system, with m 25 kg...
Problem # 4 15 points The base of a damped spring-mass system, with m 25 kg and k 2500 N/m, is subjected to a harmonic excitation y(t) Xo cos ω. The amplitude of the mass is found to be 0.05 m when the base is excited at the natural frequency of the system with Yo 0.0 m. Determine the damping constant of the system.
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
7. 150 points) A one-degree-of-freedom system is shown below. (a) (50 points) Derive the differential equation governing the motion of the system usingq, the (b) (25 points) what are the natural frequency and damping ratto of the system? c) (25 points) Mc)-0 (d) (25 points) (e) (25 points) If M(t) =1.2 sin m N clockwise angular displacement of the disk from equilibrium as the generalized coordinate. 10° and the system is given an initial angulan released from rest what is...
1. A two story building is represented in the figure below by a lumped mass systen in which m1 = m2 and k1 = k2. The ground is given a harmonic motion y Ysin at. Draw the appropriate free body diagrams. (5 points) a. b. Write the equations of motion in matrix form. (5 points) c. Solve for the natural frequencies and mode shapes. (10 points) d. Solve for the displacement amplitude response of xi and x2. (10 points)
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
418. The e spring k and the dashpot c of the accompanying diagram are fastened together at A; x represents the absolute displacement of m, and y is the abso- lute displacement of the point A. The motion o (a) Construct the free-body diagram for m. (b) Write the differential equation of motion for m (c) Obtain the solution for the steady-state motion of m. (d) Determine the relation for the impressed force at A. A is defined by y-...
Problem # 4 15 points The base of a damped spring-mass system, with m 25 kg and k 2500 N/m, is subjected to a harmonic excitation y(t) Xo cos ω. The amplitude of the mass is found to be 0.05 m when the base is excited at the natural frequency of the system with Yo 0.0 m. Determine the damping constant of the system.
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