control lab 6

T'sec In helical spring experiment a student plotted the graph of T2 versus the oscillating mass (M), and Used the slope to find the spring :constant, the value of k is 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 O. O a. 13.3 N/m O b. 6.8N/m O c. 5 N/m O d. 3.3 N/m O e. 24 N/m 5 10 15 20 25 30 35 40 45 50 55 60 65 M (9) 70 75 80

B) Analyze the following frequency responses of a first-order system subject to a simple periodic input of the form Asin(wt). 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.01 0.10 L 1.00 τω 10.00 0 -2 -10 -20 100.00 0 -10 -20 -30 -40 -50 -60 -70 -80 -90 0.01 0.1 1.0 TW 10.0 100.0 C) Which would you expect to be better suited to measure a time-dependent temperature, a thermal sensor (e.g., a thermocouple) having a small diameter spherical bead or one having a large diameter spherical bead? Explain your choice using a mathematical expression or model. D) Determine the 95 % response time for the system 5 y + 5y = U(t), where, U(t) = { iftst 1 t'

please answer and explain

What mathematical relationship exists between the wave speed and the density of the medium, using the POWER trendline equation from the graph? Make your response specific (i.e., describe the full mathematical proportionality between the two variables) Feel free to use the table. Table:  Frequency (Hz) Density (kg/m) Tension (N) Speed (cm/s) Wavelength (cm) 0.85 0.1 4.0 632.5 744.12 0.85 0.7 4.0 239.0 281.18 0.85 1.3 4.0 175.4 206.35 0.85 1.9 4.0 145.1 170.70

The stress profile shown below is applied to six different biological materials: Log Time (s] The mechanical behavior of each of the materials can be modeled as a Voigt body. In response to o,= 20 Pa applied to each of the six materials, the following responses are obtained: 2 of Maferial 6 Material 5 0.12 0.10 Material 4 0.08 Material 3 0.06 0.04 Material 2 0.02 Material 1 (a) Which of the materials has the highest Young's Modulus (E)? Why? Log Time (s) (b) Using strain value of 0.06, estimate the coefficient of viscosity (n) for Material 6. Stress (kPa) Strain

A mechanical system is presented as below. There are four simulation graphs for different values for m, b and c tested for a step response. Identify the graph for m=4 kg, b=0.3 N.s/m and k=1 N/m (Hint: you may need to use matlab simulation to find it). m 1.8 1.6 1.4 b ·f(t) Step Response

plz ansswer q1 part e velocity is in km/h  not in m/s

Lab 2-Measurement Asynch - Tagged.pdf Page 4 of 7 ? Part I: Taking Measurements & Estimating Uncertainties for a single measurement www.stefanelli.eng.br The mass of the object is_ 0 i Parts on a tripie peam palance 0 0 10 20 30 1 100 2 3 40 200 4 +/- 50 60 70 5 300 7 400 80 Qv Search 8 90 9 500 100 9 10 g www.stefanelli.eng.br

find initial velocity using following equation:

In matlab code

A single degree-of-freedom linear elastic structure was subjected to a series of harmonic excitations, one at a time. The excitations had the same forcing magnitude but different forcing frequency. Forcing frequencies and observed peak steady-state displacements are shown in the graph below. Find the natural period and damping ratio of the structure. Displacement (mm) 60 50 40 30 20 10 0 0 1 2 . 3 4 Forcing frequency, f [Hz] 5 4. 6 7

The governing equation of motion for a base motion system is given by (assume the units are Newton) mä(t)+ci(t)+kx(t) =cY@, cos(@,t) +kY sin(@t) %3D Given that m = 180 kg, c = 30 kg/s, Y = 0.02 m, and о, — 3.5 rad/s %3| 1. Use Excel or Matlab to find the largest value of the stiffness, k that makes the transmissibility ratio less than 0.85 2. Using the value of the stiffness obtained in part (1), determine the transmitted force to the base motion system using Matlab or Excel. 3. Display and discuss your results.

is a mass hanging by a spring under the influence of gravity. The force due to gravity, Fg, is acting in the negative-y direction. The dynamic variable is y. On the left, the system is shown without spring deflection. On the right, at the beginning of an experiment, the mass is pushed upward (positive-y direction) by an amount y₁. The gravitational constant g, is 9.81 m/s². DO C.D Frontly у Your tasks: No Deflection m k Fg = mg Initial Condition y m k Write down an expression for the total energy If as the sum Write down an expression for the total energy H Fg = mg Figure 3: System schematic for Problem 4. Yi & X Write down, in terms of the variables given, the total potential energy stored in the system when it is held in the initial condition, relative to the system with no deflection. as the sum of potential and kinetic energy in terms of y, y, yi C After the system is released, it will start to move. Write down an expression for the kinetic energy of the system, T, in terms of…

An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x = 0 where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is the mass of the object, and k is the spring constant. A mass of 3 kilograms stretches the spring 0.2 meters. dt² Use this information to find the spring constant. (Use g = 9.8 meters/second²) m k = + kx The previous mass is detached from the spring and a mass of 17 kilograms is attached. This mass is displaced 0.45 meters below equilibrium and then launched with an initial velocity of 2 meters/second. Write the equation of motion in the form x(t) = c₁ cos(wt) + c₂ sin(wt). Do not leave unknown constants in your equation. x(t) = Rewrite the equation of motion in the form ä(t) = A sin(wt + ), where 0 ≤ ¢ < 2π. Do not leave unknown constants in your equation. x(t) =

Fluid mechanics I

Can you help me solve the following problem in MATLAB?

100 80 60 40 20 0.002 0.004 0.006 0.008 0.01 0.012 Strain, in/in. FIGURE P1.17 1.18 Use Problem 1.17 to graphically determine the following: a. Modulus of resilience b. Toughness Hint: The toughness (u) can be determined by calculating the area under the stress-strain curve u = de where & is the strain at fracture. The preceding integral can be approxi- mated numerically by using a trapezoidal integration technique: u, = Eu, = o, + o e, - 6) %3D c. If the specimen is loaded to 40 ksi only and the lateral strain was found to be -0.00057 in./in., what is Poisson's ratio of this metal? d. If the specimen is loaded to 70 ksi only and then unloaded, what is the permanent strain? Stress, ksi