All categories

2 years ago

Compute the solution to x + 2x + 2x = 0 for Xo = 0 mm, vo = 1 mm/s and write down the closed-form expression for the response.

Engineering

1 answer:

Nutka1998 [239]2 years ago

6 0

Answer:

β = $\frac{c}{\sqrt{km} }$ = 0.7071 ≈ 1 ( damping condition )

closed-form expression for the response is attached below

Explanation:

Given : x + 2x + 2x = 0 for Xo = 0 mm and Vo = 1 mm/s

computing a solution :

M = 1,

c = 2,

k = 2,

Wn = $\sqrt{\frac{k}{m} }$ = $\sqrt{2}$

next we determine the damping condition using the damping formula

β = $\frac{c}{\sqrt{km} }$ = 0.7071 ≈ 1

from the condition above it can be said that the damping condition indicates underdamping

attached below is the closed form expression for the response

You might be interested in

Air at 2.5 bar, 400 K is extracted from a main jet engine compressor for cabin cooling. The extracted air enters a heat exchange

Shkiper50 [21]

Answer:

a) Power developed by the turbine = 132.89 kW

b) magnitude of the rate of heat transfer from the air to the ambient, in kw = 251.25 kW

Explanation:

b) The process is a constant pressure process (Isobaric process)

The constant pressure specific heat of air, $c_{p} = 1.005 kJ/kg -K$

Specific heat ratio for air, $\gamma = 1.4$

The mass flow rate of air, $\dot{m} = 2.5 kg/s$

P₁ = 2.5 bar, T₁ = 400 K

P₂ = 2.5 bar, T₂ = 300 K

Using the steady flow energy equation:

$Q_{1-2} = \dot{m} c_{p} (T_{2} - T_{1} \\Q_{1-2} = 2.5 * 1.005 * (300 - 400)\\Q_{1-2} = -251.25 kW$

Therefore, the magnitude of the rate of heat transfer from the air to the ambient, in kw, $Q_{1-2} = 251.25 kW$

a) For the isentropic process:

Power developed by the turbine is given by the relation $\dot{W} = \dot{M} c_{p} (T_{2} - T_{3})$

Isentropic efficiency, $\eta_{t} = 80%$

P₂ = 2.5 bar, T₂ = 300 K

P₃ = 1 bar, $T_{3s}$ = ? where $T_{3s}$ is the isentropic temperature at 100% efficiency

The isentropic relation is given by:

$\frac{T_{3s} }{T_{2} } = (\frac{P_{3} }{P_{2} }) ^{\frac{\gamma - 1}{\gamma} } \\\frac{T_{3s} }{300 } = (\frac{1 }{2.5 }) ^{\frac{1.4 - 1}{1.4 }$

$T_{3s} = 230.9 K$

To get the temperature at 80% efficiency, we will use the relation:

$\eta_{t} = \frac{T_{2} - T_{3} }{T_{2} - T_{3s} } \\0.8= \frac{300 - T_{3} }{300 - 230.9 }$

T₃ = 244.72 K

Power developed by the turbine is given by the relation:

$\dot{W} = \dot{M} c_{p} (T_{2} - T_{3})\\ \dot{W} = 2.5 * 1.005* (300-244.72)\\ \dot{W} = 138.89 kW$

4 0

2 years ago

Read 2 more answers

The following median grain size data were obtained during isothermal liquid phase sintering of an 82W-8Mo-8Ni-2Fe alloy. What is

Morgarella [4.7K]

Answer:

The probable grain-coarsening mechanism is : Ideal grain growth mechanism

( $d^{2}$ - $d_{0} ^{2}$ = kt )

Explanation:

The plot attached below shows the time dependence of the growth of grain.

The probable grain-coarsening mechanism is : Ideal grain growth mechanism

the ideal growth follows this principle = $d^{2} - d^{2} _{0}$ = kt

d = final grain size

$d_{0}$ = initial grain size

k = constant ( temperature dependent )

t = 0

8 0

3 years ago

A 40kg steel casting (Cp=0.5kJkg-1K-1) at a temperature of 4500C is quenched in 150kg of oil (Cp=2.5kJkg-1K-1) at 250C. If there

podryga [215]

Of the oil I hope this help

4 0

3 years ago

The electron beam in a TV picture tube carries 1015 electrons per second. As a design engineer, determine the voltage needed to

leonid [27]

Answer:

The voltage needed to accelerate the electron beam is 2.46 x 10^16 Volts

Explanation:

The rate of electron flow is given as:

q = 1015 electrons per second

The total current is given by:

Total Current = (Rate of electron flow)(Charge on one electron)

Total Current = I = (1015 electrons/s)(1.6 x 10^-19 C/electron)

I = 1.624 x 10^-16 A

Now, we know that electric power is given as:

Electric Power = Current x Voltage

P = IV

V = P/I

V = 4 W/1.624 X 10^-16 A

<u>V = 2.46 x 10^16 Volts</u>

6 0

2 years ago

3. When starting an automatic transmission

Alexxandr [17]

Answer:

It should be in Park or Neutral.

Explanation:

4 0

3 years ago