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A vibratory system can be modeled as a mass spring dashpot system as shown in Figure. In a free vibration test, the mas...
Frequency Response of a mass-spring-dashpot system Consider a mass-spring-dashpot system driven b...
Use matlab for the following:
Frequency Response of a mass-spring-dashpot system Consider a mass-spring-dashpot system driven by a unit amplitude harmonic input mdx/dt+ cdx/dt + kx- Sin (wt) Use Matlab to simulate time response for ten well-chosen values of w for 3 different values of dimensionless damping factor : 0, between 0 and 1, larger than 1. Record and plot the steady state values of amplitude.
Frequency Response of a mass-spring-dashpot system Consider a mass-spring-dashpot system driven by a unit...
Consider a driven oscialting spring-mass system modeled by my' + by' + ky = Fo cos(wt)....
Consider a driven oscialting spring-mass system modeled by my' + by' + ky = Fo cos(wt). Find the N resonant frequency of a spring-mass system with mass 3 kg, a spring constant of 10 , and viscous Ns damping whose coefficient is 6 m wolv
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...
A single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300...
A single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300 Ns/m, and spring constant of 5000 N/m, is subjected to periodic displacement excitation u(t) as shown in the figure below. 1. Derive the equation of motion 2. Using Laplace transform, find characteristic equation. 3. Find the undamped and damped natural frequencies. 4. Find the damping ratio. 5. Find the transfer function of output x(t) to the periodic input u(t) using Laplace transform.
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two per...
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two periods for the case when Wn-2rad/s, 괴,-1mm, and eto =-v/5mm/s. 2. (introduction) The approximation sin θ ะ θ is reasonable for θ < 10°. If a pendulum of length 0.5m, has an initial position of 0()0, what is the maximum value of the initial angular velocity that can be given to the pendulum without violating this smll angle approximation? 3. (harmonic...
An automobile suspension system is modeled as a 2-DoF vibration system as shown in Figure below...
An automobile suspension system is modeled as a 2-DoF
vibration system as shown in Figure below
Derive the equation of motion
Determine the natural frequencies of the automobile
with the following data
Mass (mm) = 1000kg1000kg
Momen of inertia (ImIm) = 450kgm2450kgm2
Distance between front axle and C.G. (LfLf) =
1.2m1.2m
Distance between rear axle and C.G. (LfLf) =
1.5m1.5m
Front spring stiffnes (kfkf) = 18kN/m18kN/m
Rear spring stiffnes (krkr) = 17kN/m17kN/m
Front damper coefficient (cfcf) =
3kNs/m3kNs/m
Rear damper...
3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following seco...
3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following second order linear ODE: dx,2 dt n dt2 (0) C dt where is the damping ratio an wn is the natural frequency, both related to k, b, and m (the spring constant, damping coefficient, and mass, respectively) (a) Use the forward difference approximations of (b) Using Δt andd to obtain a finite difference formula for x(t+ 2Δ) (like we did in class for the...
The landing gear of an airplane can be idealised as the spring-mass-damper system shown in the...
The landing gear of an airplane can be idealised as the spring-mass-damper system shown in the figure below. If the runway surface is described by y() = Ycoswt, determine the value of the damping coefficient c that gives an amplitude of vibration of the airplane of 1.0 mm. Assume m 153 rad/s. 1.8 mm, and w 2200 kg, k 4.9 MN/m, Y = x(e) Housing with strut and viscous damping Mass of aircraft y(e) Runway ww.
Use matlab for the following:
Frequency Response of a mass-spring-dashpot system Consider a mass-spring-dashpot system driven by a unit amplitude harmonic input mdx/dt+ cdx/dt + kx- Sin (wt) Use Matlab to simulate time response for ten well-chosen values of w for 3 different values of dimensionless damping factor : 0, between 0 and 1, larger than 1. Record and plot the steady state values of amplitude.
Frequency Response of a mass-spring-dashpot system Consider a mass-spring-dashpot system driven by a unit...
Consider a driven oscialting spring-mass system modeled by my' + by' + ky = Fo cos(wt). Find the N resonant frequency of a spring-mass system with mass 3 kg, a spring constant of 10 , and viscous Ns damping whose coefficient is 6 m wolv
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...
A single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300 Ns/m, and spring constant of 5000 N/m, is subjected to periodic displacement excitation u(t) as shown in the figure below. 1. Derive the equation of motion 2. Using Laplace transform, find characteristic equation. 3. Find the undamped and damped natural frequencies. 4. Find the damping ratio. 5. Find the transfer function of output x(t) to the periodic input u(t) using Laplace transform.
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two periods for the case when Wn-2rad/s, 괴,-1mm, and eto =-v/5mm/s. 2. (introduction) The approximation sin θ ะ θ is reasonable for θ < 10°. If a pendulum of length 0.5m, has an initial position of 0()0, what is the maximum value of the initial angular velocity that can be given to the pendulum without violating this smll angle approximation? 3. (harmonic...
An automobile suspension system is modeled as a 2-DoF
vibration system as shown in Figure below
Derive the equation of motion
Determine the natural frequencies of the automobile
with the following data
Mass (mm) = 1000kg1000kg
Momen of inertia (ImIm) = 450kgm2450kgm2
Distance between front axle and C.G. (LfLf) =
1.2m1.2m
Distance between rear axle and C.G. (LfLf) =
1.5m1.5m
Front spring stiffnes (kfkf) = 18kN/m18kN/m
Rear spring stiffnes (krkr) = 17kN/m17kN/m
Front damper coefficient (cfcf) =
3kNs/m3kNs/m
Rear damper...
3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following second order linear ODE: dx,2 dt n dt2 (0) C dt where is the damping ratio an wn is the natural frequency, both related to k, b, and m (the spring constant, damping coefficient, and mass, respectively) (a) Use the forward difference approximations of (b) Using Δt andd to obtain a finite difference formula for x(t+ 2Δ) (like we did in class for the...
The landing gear of an airplane can be idealised as the spring-mass-damper system shown in the figure below. If the runway surface is described by y() = Ycoswt, determine the value of the damping coefficient c that gives an amplitude of vibration of the airplane of 1.0 mm. Assume m 153 rad/s. 1.8 mm, and w 2200 kg, k 4.9 MN/m, Y = x(e) Housing with strut and viscous damping Mass of aircraft y(e) Runway ww.
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