Find the motion of the mass-spring system modeled by the ODE and initial conditions. Sketch or graph the solution curve. In addition, sketch or graph the curve of $y-y_p$ to see when the system practically reaches the steady state.

$\left(D^2+2 D+I\right) y=75\left(\sin t-\frac{1}{2} \sin 2 t+\frac{1}{3} \sin 3 t\right)$, $y(0)=0 . \quad y^{\prime}(0)=1$

As shown in figure, a silicon chip measuring $5 \mathrm{~mm}$ on a side and $1 \mathrm{~mm}$ in thickness is embedded in a ceramic substrate. At steady state, the chip has an electrical power input of $0.225 \mathrm{~W}$. The top surface of the chip is exposed to a coolant whose temperature is $20^{\circ} \mathrm{C}$. The heat transfer coefficient for convection between the chip and the coolant is $150 \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}$. Heat transfer by conduction between the chip and the substrate is negligible. Determine (a) the surface temperature of the chip, in ${ }^{\circ} \mathrm{C}$, and (b) the rate of exergy destruction within the chip, in W. What causes the exergy destruction in this case? Let $T_0=293 \mathrm{~K}$.

Escojan a cuatro personas famosas de la politica, del cine o de la televisión sin dar su nombre. Luego, túrnense para describir a cada persona. Su compañero/a debe tratar de adivinar quién es. El desafío está en usar el mayor número de palabras de ¡Así lo decimos!

En grupos pequeños, expresen sus opiniones sobre lo siguiente. Usa el subjuntivo para expresar dudas.

modelo:

________ es la mejor tienda de música de nuestra ciudad.

Compañero 1: Si, creo que Musicworld es la mejor tienda de música de nuestra ciudad.

Compañero 2: No, dudo que Musicworld sea la mejor tienda de música de nuestra ciudad.

• ________ son los jeans más populares.

A $\it{flow~ calorimeter}$ is used to measure the specific heat of a liquid. Heat is added at a known rate to a stream of the liquid as it passes through the calorimeter at a known rate. Then a measurement of the resulting temperature difference between the inflow and the outflow points of the liquid stream enables us to compute the specific heat of the liquid. A liquid of den- sity $0.85$ g/cm$^3$ flows through a calorimeter at the rate of $8.2$ cm$^3$/s. Heat is added by means of a $250$-$\mathrm{W}$ electric heat- ing coil, and a temperature difference of $15\degree\mathrm{C}$ is established in steady-state conditions between the inflow and the outflow points. Find the specific heat of the liquid.

Researchers in New Zealand interviewed 907 drivers at age 21. The researchers had data on previous traffic accidents and asked the drivers about marijuana use. Here are data on whether these drivers had caused accidents at age 19, broken down by marijuana use at that age.

$$\begin{array} {lc} & \text{Frequency of marijuana use per year} \\ \text {Caused accident} &\begin{array}{c|c|c|c|c|c} & \text { Never } & 1-10 \text { times } & 11-50 \text { times } & 51+\text { times } & \text { Total } \\ \hline \text { No } & 393 & 193 & 55 & 106 & 747 \\ \hline \text { Yes } & 59 & 36 & 15 & 50 & 160 \\ \hline & 452 & 229 & 70 & 156 & 907 \end{array} \\ \end{array}$$

Make a segmented bar chart to determine if there is an association between these variables.

A flow calorimeter is a device used to measure the specific heat of a liquid. Energy is added as heat at a known rate to a stream of the liquid as it passes through the calorimeter at a known rate. Measurement of the resulting temperature difference between the inflow and the outflow points of the liquid stream enables us to compute the specific heat of the liquid. Suppose a liquid of density 0.85 g/cm³ flows through a calorimeter at the rate of 8.0cm³/s. When energy is added at the rate of 250 W by means of an electric heating coil, a temperature difference of 15 C° is established in steady-state conditions between the inflow and the outflow points.What is the specific heat of the liquid?

Masters Golf Products, Inc., spent 3 years and $\$ 1,000,000$ to develop its new line of club heads to replace a line that is becoming obsolete. To start manufacturing them, the company will have to invest $\$ 1,800,000$ in new equipment. The new clubs are expected to generate an increase in operating cash inflows of $\$ 750,000$ per year for the next 10 years. The company has decided that the existing line could be sold to a competitor for $\$ 250,000$. a. How should the $\$ 1,000,000$ in development costs be classified?

Fill in the missing entries of the stochastic matrix

$$P=\left[\begin{array}{ccc}{\frac{1}{3}} & {\frac{1}{12}} & {\frac{1}{6}} \\ {*} & {\frac{1}{6}} & {*} \\ {\frac{1}{6}} & {*} & {\frac{1}{2}}\end{array}\right]$$

and find its steady-state vector.

Figure shows a solar collector panel embedded in a roof. The panel, which has a surface area of $24\ \mathrm{ft}^2$, receives energy from the sun at a rate of $200\ \mathrm{Btu} / \mathrm{h}$ per $\mathrm{ft}^2$ of collector surface. Twenty-five percent of the incoming energy is lost to the surroundings. The remaining energy is used to heat domestic hot water from $90$ to $120^{\circ} \mathrm{F}$. The water passes through the solar collector with a negligible pressure drop. Neglecting kinetic and potential effects, determine at steady state how many gallons of water at $120^{\circ} \mathrm{F}$ the collector generates per hour.

The seismic instrument is mounted on a structure which has a vertical vibration with a frequency of 5 Hz and a double amplitude of 18 mm. The sensing element has a mass m = 2 kg, and the spring stiffness is k = 1.5 kN/m. The motion of the mass relative to the instrument base is recorded on a revolving drum and shows a double amplitude of 24 mm during the steady-state condition. Calculate the viscous damping constant c.

Use the following information. A man owns an Audi, a Ford, and a VW. He drives every day and never drives the same car two days in a row. These are the probabilities that he drives each of the other cars the next day:

$\operatorname{Pr}($ Ford after Audi $)=0.7 \quad \operatorname{Pr}(\mathrm{VW}$ after Audi $)=0.3$ $\operatorname{Pr}($ Audi after Ford $)=0.6 \quad \operatorname{Pr}(\mathrm{VW}$ after Ford $)=0.4$ $\operatorname{Pr}($ Audi after VW) $=0.8 \quad \operatorname{Pr}($ Ford after $\mathrm{VW})=0.2$

What is the steady-state vector for this problem?

A counter-rotating eccentric mass exciter consisting of two rotating $14 \mathrm{~oz}$ weights describing circles of $6 \mathrm{~in}$. radius at the same speed but in opposite senses is placed on a machine element to induce a steady-state vibration of the element and to determine some of the dynamic characteristics of the element. At a speed of $1200 \mathrm{~rpm}$, a stroboscope shows the eccentric masses to be exactly under their respective axes of rotation and the element to be passing through its position of static equilibrium. Knowing that the amplitude of the motion of the element at that speed is $0.6 \mathrm{~in}$. and that the total weight of the system is $300 \mathrm{~lb}$, determine $(a)$ the combined spring constant $k$, $(b)$ the damping factor $c / c_c$.

Air enters the turbine of a jet engine at 1190 K, 10.8 bar and expands to 5.2 bar. The air then flows through a nozzle and exits at 0.8 bar. Operation is at steady state, and the flow is adiabatic. The nozzle operates with no internal irreversibilities, and the isentropic turbine efficiency is 85%. The air velocities at the turbine inlet and exit are negligible. Assuming the ideal gas model for the air, determine the velocity of the air exiting the nozzle, in m/s.