lab 5

The response of a certain dynamic system is given by: x(t)=0.003 cos(30t) +0.004 sin(30r) m   (5Mks)   Determino:   (i) the amplitude of motion.   (2Mks)   (ii) the period of motion.   (in) the linear frequency in Hz.   (4) the angular frequency in rad/s.   (2Mks) (2Mks)   (2Mks) (2Mks)   (v) the frequency in cpm.   (vi) the phase angle.   (2Mks)   (vii) the response of the system in the form of x(t) = X sin(t +$) m.

r:09 moodle1.du.edu.om An application demands that sinusoidal pressure variation of 250 Hz be measured with no more than 2% dynamic error. In selecting a suitable pressure transducer from vendor catalog, you note that a desirable line of transducer has a fixed natural frequency of 500 Hz but that you have a choice of transducer damping ratio of between 0.5 and 1.5 in increments of 0.05. select a suitable transducer. The value of damping ratio is between the following values Select one: O a. 0.707 and 0.807 O b. 0.631 and 0.692 c. 0.2356 and 0.5625 d. 0.5215 and 0.5625 Previous page Next page 1 Assignmen II

16:55 M O X * 16% £ Jihad Harfosh 20 minutes ago In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, O"max, to the maximum angular velocity, O'max, is rt s^(-1). What is the time needed for the pendulum to complete one-half ocillation? 4 sec 0.5 sec 1 sec 2 sec 0.25 sec く

K Kt m₂ mi For this fig. > with damping Find the following: ~Equations of motion C ~Mass matrix ~Stiffness matrix ~Damping matrix ~Natural freqyancy ~All damping properties.. 72 ZI

i. Derive the linear and quatratic approximation of the below resistance temperature readings(temperature from 40 °c to 80 °c). (. ii. find out the resistance of RTD at a temperature of 200°c using linear approximation? ( Temperature 40 45 50 55 60[TO] 65 70 75 80 Resistance ohm 115.239 120.521 167.096 254.966 384.13 554.587 766.34 1019.38 1313.724

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

ent #damping- Sear X dynamics systems questions 1[1 X + To File C:/Users/40332698/AppData/Local/Packages/microsoft windowscommunicationsapps_8wekyb3d8bbwe/LocalState/Files/50/145/Attachments/dynamics%... + ? A Read aloud Add textDraw Page view Highlight Erase V Q 2/60 At time t = 0, the position vector of a particle mov- ing in the x-y plane is r = 5i m. By time t = 0.02 s, its position vector has become 5.1i+ 0.4j m. Determine the magnitude vav of its average veloc- ity during this interval and the angle 0 made by the average velocity with the positive x-axis. Type here to search O Bi 2 € P T 9°C Cloudy D4 ^ Je e F2 end prt sc F10 delete E 3 E I IL C D sex $ R F + 2 5 T G B A 6 Y H BR & 7 N Å U J FB * 8 M 1 F9 K ( 9 O ) O L home P - : ; F12 { + 1 insert e 1 -

6. A ball is thrown straight up in the air at time t = 0. Its height y(t) is given by y(t) = vot - 791² (1) Calculate: (a) The time at which the ball hits the ground. First, make an estimate using a scaling analysis (the inputs are g and vo and the output is the time of landing. Think about their units and how you might construct the output using the inputs, just by matching units). Solve the problem exactly. Verify that the scaling analysis gives you (almost) the correct answer. (b) The times at which the ball reaches the height v/(4g). Use the quadratic formula. (c) The times at which the ball reaches the height v/(2g). You should find that both solutions are identical. What does this indicate physically? (d) The times at which the ball reaches the height v/g. What is the physical interpretation of your solutions? (e) Does your scaling analysis provide any insight into the answers for questions (a-e)? Discuss. (Hint: Observe how your answers depend on g and vo).

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

PIoVide ue comect u We want to design an experiment to measure oscillations of a simple pendulum on the surface of Jupiter with acceleration due to gravity g= 30 ms 2. We have to make do with a rudimentary video camera with a frame rate of 15 Hz to record oscillations in a pendulum and use it to measure the frequency of oscillation. The smallest length of the pendulum that we can send so that the correct oscillation frequency can be measured is cm. Assume perfect spatial resolution of the camera and ignore other "minor" logistical difficulties with this experiment.

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

The partial di§erential equation for the small-amplitude vibrations of a string of length ` is given by A@2y@t2T@2y@x2 = 0 where y(x; t) is the vibration amplitude,  is the material density of the string, A is the string cross sectional area, and T is the tension force in the string. Using only the parameters given, make this equation dimensionless. Hint 1: first find a combination of ` and/or  and/or A and/or T to make x, y, and t dimensionless.(It is clear that a different combination will be needed to make t dimensionless than that for x and y.) Hint 2: let c = q TA . What are the dimensions of c? (Note that c is known as the ìwave speed.î)

3. Problem Estimate the frictional resistance Rp for a container ship using the ITTC 1957 model-ship correlation line Equation (2): 0.075 CF [ log,,(Re) – 21 The ship has the following particulars: Full scale ship data length between perpendiculars Lep length in waterline length over wetted surface 195.40 m Lwz Los For the wetted surface S you can use the following formula by Kristensen and Lützen (2012) derived for container ships. 200.35 m 205.65 m breadth B 29.80 m draft T 10.10 m 37085.01 m3 S = 5 + Lw. T 0.995 displacement design speed Again, use the most up-to-date ITTC water properties sheet for density and kinematic viscosity. V 21.00 kn

1) Consider the baseband pulse x(1) = n(2) = 11 a) Derive the complex ambiguity function for x(t) and compare your result with the one obtained in class. b) Use MATLAB to compute the complex ambiguity function and compare it to part (a). c) Now, consider the pulse x(t) = sinc(Bt) i) Derive the complex ambiguity function for x(t) and compare to the ambiguity function of the rect pulse. Make your observations. ii) Plot the ambiguity function using the mesh function and using the contour function. iii) Use MATLAB to compute the complex ambiguity function and compare it to part (ii).

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) =

22°F Clear 1MMBU BU ► ► ► 20°HD®°°*EqqaHÛDin × ODE DDE DE DE File C:/Users/ignor/Downloads/Assignment%203%20(2).pdf T❘ Read aloud Ask Copilot Draw a) Use Newton's second law b) Use the Torque equation /// Collar A is free to slide with negligible friction on the circular guide mounted in a vertical frame. Find the EOM of collar A if the frame is given a velocity v and a constant horizontal acceleration a to the right. Search 1 A www of 6 TTTT | CD a laaa 8 o + ENG 60 T N 7:35 PM 1/17/2024 x

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

5 Problem Match the following two frequency response diagrams: -0 0.4 |G(i w)| 0.2 10 |G(i w)| 5 Response A 2 3 4 5 6 7 8 Frequency, (rad/s) Response B 5 6 7 8 Frequency, w(rad/s) 1 2 3 4 6 6 10 10 10 to two of the following ODES 1. +x+100x = u(t) 5. +100x = u(t) 9. +100x = u(t) 3. x+x+5x= u(t) 4. x+x+x= u(t) 2. x+x+25x = u(t) : 6. x + 25xu(t) 10. +25x = u(t) 7. x+5x= u(t) 8. u(t) 11. +5x= u(t) = 12. xu(t)

+ a si diplacement #damping-Sear x dynamics systems questions 111 X Q V Highlight File C/Users/40332698/AppData/Local/Packages/microsoft windowscommunicationsapps_8wekyb3d8bbwe/LocalState/Files/50/145/Attachments/dynamics%... Page view A Read aloud | Add textDraw Q 8 of 40 a 2/59 At time t = 10 s, the velocity of a particle moving in the x-y plane is v= 0.1i+2j m/s. By time = 10.1 s, its velocity has become -0.1i + 1.8j m/s. Determine the magnitude aav of its average acceleration during this interval and the angle 0 made by the average accel- eration with the positive x-axis. Type here to search O H T JU E # 2 W S 3 E D C Ix $ R 5 T OL G F FO 6 Y H N & 7 U J 8 I K 9 prt sc O O L home P 1 + 11 To 1 Erase 12 E 9°C Cloudy D

Thermocouples are devices used to measure temperature of a given sample or the surroundingmedium. These devices feature a “bead”, which has a spherical shape, and produces voltage upon changein temperature. For an engineering application at a pharmaceutical company, thermocouple devices arebeing tested for their responsiveness, i.e. how fast it can detect temperature changes in the environment(surrounding air). The engineers at this company have specified design constraints for an idealthermocouple: it must detect temperature changes no later than 1.5 minute, and the reportedtemperature value must be reasonably correct: at most %3 difference between measured and actualtemperature values is allowed.Four thermocouples from different vendors are being tested. Relevant properties of these devices arelisted below: The experiment involves placing the thermocouple from air at 20 °C to air at 150 °C, and monitoring thetime it takes for the measured values to reach 150 °C, which is the…

a) Vortex shedding is a common fluid flow problem across bluff bodies. The design of buildings and bridges take into account the analysis of vortex shedding phenomena to avoid the occurrence of resonance, where the natural frequency of the body matches the vortex shedding frequency. In this analysis, the following parameters are found to be important: velocity of flow (V), density of fluid (p), hydraulic diameter of the duct (D₁), dynamic viscosity of fluid (u), width of body (B) and the vortex shedding frequency (n). Using the method of repeating variables, find the non-dimensional relationship governing the phenomena.

A seismic transducer with natural frequency 750 rad/s and damping ratio 0.7 is used to measure acceleration. The input to the sensor is a sinusoidal displacement with amplitude 1 x 10 m and fundamental frequency 100 Hz. The resulting steady-state acceleration measurement is a sinusoid. What is its amplitude (in m/s?)?

Consider a second order system given by 10 d²x(t)/df² + 6 dx(t)/dt + 42 x(t) = 4 cost. What is the natural frequency in rad/s? Do not include units. Write your answer in scientific notation using 3 significant figures. (eg. 1.23e1)

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

(Q-4) Balance the meter stick with two weights and a rock. 0 cm 100 cm Jrock 100g position (cm) weight (gwt) lever arm (cm) torque (gwt cm) Rock 10.60 XXXXXX XXXXXXXX Weight 1 구군, 60 150 cw Weight 2 93.5 100 (Q-5) Assume that the torques balance and use this fact to calculate the weight of the rock. Z Tecw Złcw = Wrack

2) A device used in a ground radar system has age to failure that is described approximately by a Weibull distribution with mean life 83 h, shape parameter 1.5, and location parameter zero. When it fails it takes on average 3.5 h to repair: a) Calculate the reliability over a 25 h period, and the 'steady state' availability of the device. b) Calculate the reliability over 25 h, and the ‘steady state' availability of a subsystem that consists of two of these devices in active parallel redundancy.

An aircraft wing is modelled by using a specific element which composed of 2 nodes as shown below. Each node of this element has 1 degree of freedom. If the total nodes used within the model be equal to 2,690, calculate the total degree of freedom of the system. element Node 1 Node 2 Your Answer: Answer

Harmonic oscillators. One of the simplest yet most important second-order, linear, constant- coefficient differential equations is the equation for a harmonic oscilator. This equation models the motion of a mass attached to a spring. The spring is attached to a vertical wall and the mass is allowed to slide along a horizontal track. We let z denote the displacement of the mass from its natural resting place (with x > 0 if the spring is stretched and x 0 is the damping constant, and k> 0 is the spring constant. Newton's law states that the force acting on the oscillator is equal to mass times acceleration. Therefore the differential equation for the damped harmonic oscillator is mx" + bx' + kr = 0. (1) k Lui Assume the mass m = 1. (a) Transform Equation (1) into a system of first-order equations. (b) For which values of k, b does this system have complex eigenvalues? Repeated eigenvalues? Real and distinct eigenvalues? (c) Find the general solution of this system in each case. (d)…

! Required information The power P generated by a certain windmill design depends upon its diameter D, the air density p, the wind velocity V, the rotation rate 2, and the number of blades n. A model windmill, of diameter 50 cm, develops 2.7 kW at sea level when V= 40 m/s and when rotating at 4800 rev/min. What power will be developed by a geometrically and dynamically similar prototype, of diameter 5 m, in winds of 10 m/s at 2000 m standard altitude? At 2000 m altitude, p = 1.0067 kg/m3. At sea level, p= 1.2255 kg/m3. The power developed is ]KW.