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Exercise 1 Obtain expressions for the dimensions of the following quantities using both (1) the absolute...
1. In the following expressions, x and y represent lengths or positions, v represents a velocity,...
1. In the following expressions, x and y represent lengths or positions, v represents a velocity, a represents acceleration, t represents a time, m is mass, and k has the value 2m?1. Use dimensional analysis to identify the invalid relationships: (a) vf = vi+ax, (b) y = (2m) cos(kx), (c) mat = mvx, (d) 2 ln(va=vb) = 6 sin(tb=ta). 2. A certain particle's position x at a time t is given by x = ka^mt^n, where k, m, and n...
Show that the expression v = at, where v represents speed, a acceleration, and t an...
Show that the expression v = at, where v represents speed, a acceleration, and t an instant of time, is dimensionally correct. Dimensions and Units of Four Derived Quantities Quantity Area Volume Speed Acceleration Dimensions L2 L3 UT LT2 SI units m2 m m/s m/s2 U.S. customary units ft2 ft/s ft/s2 SOLUTION (Use the following as necessary: L and T.) Identify the dimensions of v from the table above: [v] - Identify the dimensions of a from the table above...
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...
Example 1 A star undergoes some mode of oscillation. Scientists/engineers have hypothesized that the oscillation frequency...
Example 1 A star undergoes some mode of oscillation. Scientists/engineers have hypothesized that the oscillation frequency (cycles per second), o, is dependent on the density p and the radius R and the gravitational constant G which appears in Newton's law of universal gravitation. If you are not familiar with the gravitational constant, read the section on mass and weight in Chapter 4 (Dimensions/units) of the text. Therefore, w has dimensions (T), and P, R, Gare the governing parameters, with dimensions...
Multivariable Calculus help with the magnitude of angular momentum: My questions is exercise 4 but I have attached exercise 1 and other notes that I was provided 4 Exercise 4. In any mechanics proble...
Multivariable Calculus help with the magnitude of angular
momentum: My questions is exercise 4 but I have attached exercise 1
and other notes that I was provided
4 Exercise 4. In any mechanics problem where the mass m is constant, the position vector F sweeps out equal areas in equal times the magnitude of the angular momentum ILI is conserved (Note: be sure to prove "if and only if") (Note: don't try to use Exercise 2 in the proof of...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s)X2 (s)/F(s) (b) Does the system oscillate with a unit step input (f (t))? Explain the reason (c) Decide if the system(x2 (t)) is stable with a unit step input (f (t))? Explain the reason 1. 320) 8 kg 2 N/m 4N-s/m 2N-s/m Fig. 1 2. There are two suspensions for a car as shown in Fig. 2 (a) Find the equations of each...
Using the force-voltage analogy shown in table 1, obtain a mechanical analogu electrical system shown above...
Using the force-voltage analogy shown in table 1, obtain a mechanical analogu electrical system shown above (4 pts) Table 1. Force-Voltage Analogy Force, p (torque T Mass, m (moment of inertia J) Viscous-friction coefficient, b Spring constant, k Displacement, x (angular displacement 6) Voltage, Inductance, L Resistance, R Reciprocal of capacitance, /C Charge, Velocity (angular velocity b) Current, i
In this problem, we will try to illustrate the following: a waggon is linked to a...
In this problem, we will try to illustrate the following: a waggon is linked to a wall with a spring and a damper. The position of the waggon is given by x(t). The waggon can move without any friction on the ground. The mass is M. (35 pnts) The differential equation that describes the system is the following: d2x M + b + cx(t) = F dt2 Where: M=5 [kg] mass of the waggon b= 1 [Ns/m] damper constant C=...
1. Express the answer to the following problems using the correct number of significant figures a....
1. Express the answer to the following problems using the correct number of significant figures a. 1.144 x 10 20.0 b. 4.77 x 101 -9.16 x 10 2. Express the Boltzmann constant (1.38065 x 102" kg m's K') in units of miles' lb yrK 3. Convert 9.997 x 101 g cm* into kg km 4. The Reynolds number is used to deseribe the conditions of particle settling If the Reynolds number is given by the following equation Where v, is...
Matlab help 1) Given the functions x1()= tu()-tuft-1) and X2(t)=10e-5,11(), do the following: 1. Plotx,(t) and x2(0) using MATLAB 2. Use MATLAB to find and plot x(0=x:@*.x2(t), where * denotes co...
Matlab help
1) Given the functions x1()= tu()-tuft-1) and X2(t)=10e-5,11(), do the following: 1. Plotx,(t) and x2(0) using MATLAB 2. Use MATLAB to find and plot x(0=x:@*.x2(t), where * denotes convolution. 3. Find x(t)=x;()*X2(1) by hand using Laplace transforms. 4. Plot the result of part 3 in MATLAB and compare it to that found in part 2. 2) Given the transfer function shown below, do the following: 1. Find the system's impulse response and plot it using MATLAB 2. Repeat...
Show that the expression v = at, where v represents speed, a acceleration, and t an instant of time, is dimensionally correct. Dimensions and Units of Four Derived Quantities Quantity Area Volume Speed Acceleration Dimensions L2 L3 UT LT2 SI units m2 m m/s m/s2 U.S. customary units ft2 ft/s ft/s2 SOLUTION (Use the following as necessary: L and T.) Identify the dimensions of v from the table above: [v] - Identify the dimensions of a from the table above...
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...
Example 1 A star undergoes some mode of oscillation. Scientists/engineers have hypothesized that the oscillation frequency (cycles per second), o, is dependent on the density p and the radius R and the gravitational constant G which appears in Newton's law of universal gravitation. If you are not familiar with the gravitational constant, read the section on mass and weight in Chapter 4 (Dimensions/units) of the text. Therefore, w has dimensions (T), and P, R, Gare the governing parameters, with dimensions...
Multivariable Calculus help with the magnitude of angular
momentum: My questions is exercise 4 but I have attached exercise 1
and other notes that I was provided
4 Exercise 4. In any mechanics problem where the mass m is constant, the position vector F sweeps out equal areas in equal times the magnitude of the angular momentum ILI is conserved (Note: be sure to prove "if and only if") (Note: don't try to use Exercise 2 in the proof of...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s)X2 (s)/F(s) (b) Does the system oscillate with a unit step input (f (t))? Explain the reason (c) Decide if the system(x2 (t)) is stable with a unit step input (f (t))? Explain the reason 1. 320) 8 kg 2 N/m 4N-s/m 2N-s/m Fig. 1 2. There are two suspensions for a car as shown in Fig. 2 (a) Find the equations of each...
Using the force-voltage analogy shown in table 1, obtain a mechanical analogu electrical system shown above (4 pts) Table 1. Force-Voltage Analogy Force, p (torque T Mass, m (moment of inertia J) Viscous-friction coefficient, b Spring constant, k Displacement, x (angular displacement 6) Voltage, Inductance, L Resistance, R Reciprocal of capacitance, /C Charge, Velocity (angular velocity b) Current, i
In this problem, we will try to illustrate the following: a waggon is linked to a wall with a spring and a damper. The position of the waggon is given by x(t). The waggon can move without any friction on the ground. The mass is M. (35 pnts) The differential equation that describes the system is the following: d2x M + b + cx(t) = F dt2 Where: M=5 [kg] mass of the waggon b= 1 [Ns/m] damper constant C=...
1. Express the answer to the following problems using the correct number of significant figures a. 1.144 x 10 20.0 b. 4.77 x 101 -9.16 x 10 2. Express the Boltzmann constant (1.38065 x 102" kg m's K') in units of miles' lb yrK 3. Convert 9.997 x 101 g cm* into kg km 4. The Reynolds number is used to deseribe the conditions of particle settling If the Reynolds number is given by the following equation Where v, is...
Matlab help
1) Given the functions x1()= tu()-tuft-1) and X2(t)=10e-5,11(), do the following: 1. Plotx,(t) and x2(0) using MATLAB 2. Use MATLAB to find and plot x(0=x:@*.x2(t), where * denotes convolution. 3. Find x(t)=x;()*X2(1) by hand using Laplace transforms. 4. Plot the result of part 3 in MATLAB and compare it to that found in part 2. 2) Given the transfer function shown below, do the following: 1. Find the system's impulse response and plot it using MATLAB 2. Repeat...
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