0 stringlengths 10 969 | label int64 0 1 |
|---|---|
**\[Change of sign]** Inverting the function results in inverting the Fourier transform: latex0 **\[Translation]** Shifting a function by a certain amount results in a phase shift: latex1 **\[Scaling]** Stretching a function by a factor latex2 results in the Fourier transform to be compressed by the same factor: latex3 **\[Derivative]** Finding the transform of a derivative simply translates into multiplication: latex4 | 0 |
A 5 cm-long fish swimming. | 0 |
Find the base current. | 1 |
Since the plates are large, it is reasonable to assume that, at least away from the edges of the plates, the flow (that is, the components latex9 , latex10 and latex11 , but not the pressure) does not depend on latex12 and latex13 (that is, it is independent of translations parallel to the plate). | 0 |
In the case of the total pressure, distinguish between isentropic and actual processes. | 1 |
Is this what you would expect according to determinant properties? | 1 |
The operational amplifier in shown below runs from power supplies of latex0 . | 0 |
**(L7/8)**: Show that the three equations, latex0 have no solutions unless latex1 , in which case they have an infinite number of solutions. | 1 |
By applying the equation derived in part (b) to the oil flow, show that: latex14 where latex15 is the gravitational acceleration, acting downward, latex16 is the pressure, latex5 is the axial coordinate positive upward (see image). | 1 |
Can the water vapour in atmospheric air be treated as an ideal gas? | 1 |
Now assume the system is damped, and that latex0 . | 0 |
Neglecting losses, what power in Kilowatts is delivered to the water by the pump? | 1 |
If latex0 and latex1 and latex2 transform to two new variables latex3 and latex4 , with latex5 and latex6 , so that latex7 , show that latex8 | 1 |
By electromagnetic theory, latex0 , and latex1 . | 0 |
Obtain the new bed configuration in equilibrium conditions. | 1 |
Sketch the step response for both the open-loop and closed-loop systems. | 1 |
(*i.e * to oscillate once every two seconds). | 0 |
A risk assessment is something that you *d*o, and then record. | 0 |
Calculate: The maximum bending moment that can be applied reversibly (i.e elastically). | 1 |
A "Busemann Biplane" consists of two identical thin aerofoils arranges as shown in the figure below, each with a deflection angle latex0 . | 0 |
The eddy viscosity in the channel can be described by (see sediment transport lectures): latex2 Obtain an expression for the depth-averaged value for latex3 by assuming that the turbulent Schmidt number latex4 . | 1 |
Find the time latex18 required for the gearwheel latex12 to attain an angular velocity of latex23 , starting from rest. | 1 |
Heat loss from the heat exchanger casing and frictional pressure drops can be neglected. | 0 |
An air conditioning unit comprises a cooling coil with condensate removal followed by an electrical heater. | 0 |
The damping constant is latex6 rad s latex5 . | 0 |
This boundary condition can be viewed as adding an image source to the original set- up. | 0 |
For simplicity, we assume air to be made of exactly the same diatomic molecules (a fair assumption) with molar mass latex2 . | 0 |
Show that the exergy destruction latex6 or irreversibility latex7 can be expressed in dimensionless form by: latex8 where latex9 and latex10 | 1 |
For liquid octane, latex0 : Assuming that water component in the combustion products is in liquid state, calculate the enthalpy of reaction at latex1 , latex2 atm burning in air. | 1 |
Suggest a simple design change to alleviate the result of part (c). | 1 |
By rearranging the equation below, calculate the wavelength of maximum absorbance of PS-I in nanometres latex1 . | 1 |
An interference pattern is formed by illuminating a pair of narrow slits, separated by 0.8 mm, with light of wavelength 500 nm. | 0 |
The pressure at the nozzle exit is gradually increased from its original value. | 0 |
Draw the circuit diagram of the potentiometer and battery setup, then add a resistor representing the load (e.g the internal resistance of the phone) Calculate the Thévenin equivalent of your power supply for latex4 no load voltage and draw the load and source characteristics. | 1 |
In Lecture 3 we derived the length contraction formula latex0 by considering the measurement of a moving rod in two frames. | 0 |
** ### Your Risk Assessment ### Your Feedback Please feel free to email Charlie Lindsay (with any comments on your experience using this exercise. | 0 |
You will have to apply Kirchhoff’s laws and set-up a set of linear equations to solve this. | 1 |
Up to now, you have applied the Bernoulli Equation *along streamlines*, assuming the flow to be steady, inviscid and with constant density. | 0 |
Allow for a latex21 “dead-band” around this value to avoid inadvertent switch-on due to low amplitude noise in the sensor signal. | 0 |
How does the time taken for the reflected path latex8 depend on latex7 ? | 1 |
The ratio of latex7 with latex1 is known as the Froude number (noted latex10 ). | 0 |
The fluid is Newtonian with density, latex6 , and dynamic viscosity, latex7 , both constant and uniform. | 0 |
An ME2 student claims that the flow at the region of maximum area of the diffuser will never become sonic, regardless of the inlet conditions. | 0 |
Show that for the centre of mass of the top to lie on the axis it is necessary that latex4 . | 1 |
**(L4)**: For two vectors in latex0 : latex1 and latex2 : Calculate latex3 . | 1 |
You may neglect viscous effects in this question. | 0 |
By integrating between the boundaries latex2 and latex3 , obtain a differential equation for the mass latex4 of the contaminant. | 1 |
Hence write the transfer function latex5 . | 1 |
Given that the Joule-Thomson coefficient for any pure substance: Show that latex0 = 0 for an ideal gas. | 1 |
By setting latex32 in the solution of the ODE that you have derived, show what this relationship is. | 1 |
Show that the work latex21 done by the position-dependent force latex7 along path 1 in the diagram above is latex23 . | 1 |
What does each ship measure for the velocities of the Earth and of the other ship? | 1 |
The shaft rotates at constant rotational speed, latex1 . | 0 |
Such flow is called free vortex.Compute the spin tensor. | 1 |
Show that in this limit latex30 where latex31 and latex22 is the intensity at latex33 . | 1 |
**\[Boas 6.10.2]** Given latex0 , integrate latex1 over the whole surface of the cube of side 1 with four of its vertices at latex2 , latex3 , latex4 , latex5 . | 1 |
The steam is compressed by the inward motion of the piston until the pressure is latex3 bar (absolute). | 0 |
**\[Boas 5.5.3]:** Find the area of the paraboloid latex0 inside the cylinder latex1 . | 1 |
Calculate the heat transfer rate from the furnace to a possible water/steam cycle, per latex5 of gas burnt (with latex1 excess air), and hence the combustion efficiency. | 1 |
Consider a surface latex0 defined as the portion of the plane latex1 with latex2 and latex3 . | 0 |
Estimate the reference height Find a value for the suspended sediment concentration, when latex6 . | 1 |
Use the scalar triple product to calculate the volume of the parallelepiped defined by latex2 , latex3 and latex6 . | 1 |
A useful approximation for the velocity profile latex5 in an incompressible laminar boundary layer, at any location along the wall, latex2 , is a sinusoidal variation from latex7 at the wall to the free stream velocity, latex8 , at the edge of the boundary layer ( latex9 ). | 0 |
Consider the equation of motion of a damped harmonic oscillator with natural frequency latex0 and damping constant latex1 , which is being driven by a time-varying external force latex2 (see Figure 5.1 in notes), latex3 Using the trial solution latex4 , show that the unknown parameters in the trial solution are, latex5 which gives you the steady state (particular) solution to the inhomogeneous differential equation. | 1 |
Calculate the minimum necessary width of the beam. | 1 |
(Note that in the response area below you can use exponential notation, e.g `5.7e13 m^(-3)` is an acceptable input - but an incorrect answer!). | 0 |
What is the position of the centre of buoyancy of the cube? | 1 |
What is the smallest mass latex5 capable of lifting latex6 ? | 1 |
Obtain an expression for the temperature ratio latex6 at the throat. | 1 |
Starting from the one-dimensional fundamental solution, obtain the time and space-dependent concentration field latex0 for this problem. | 1 |
This is the length of a so-called "seconds pendulum", which is what most long-case "grandfather clocks" have in them. | 0 |
What is the smallest number of bits which is needed to store a **complete** position measurement (rotation and translation) made using this system? | 1 |
Show that latex17 , where latex18 . | 1 |
You may assume the following: diesel contains 43 MJ/kg; the ship's diesel engines are 40% efficient; the ship's overall propulsion system is 50% | 0 |
What are the units of latex12 ? | 1 |
Note the definition of a coordinate system in the two figures. | 0 |
**(L3)** A greengrocer sells the fruits latex0 at a price latex1 (in pence). | 0 |
The small current passed by a reverse-biased ‘large area’ photodiode (having an area of latex0 and a sensitivity of latex1 ) is measured by an op-amp current to voltage amplifier stage. | 0 |
Of course, you can design as many base- latex6 systems as you wish, and you are already familiar with some of them: a clock is a sexagesimal ( latex52 ) system, and "life'' (i.e DNA) is encrypted as a quaternary system ( latex53 )! | 0 |
The area of the pipe at Point 3, just above the pump, is latex8 m latex3 and the water pressure there is latex10 Pa. | 0 |
Check your answer using the dot product. | 1 |
The atom is driven on resonance ( latex8 ) with light that has latex9 V/m. | 0 |
Two plates are placed at latex1 and at latex2 . | 0 |
A room contains air at latex0 and latex1 bar with a relative humidity of latex2 . | 0 |
Let latex3 . | 0 |
*) A different process between the same end states is adiabatic; evaluate the shaft work per unit mass of nitrogen and the change in specific entropy of the gas in this process, and determine whether it is reversible or irreversible. | 1 |
Find this value of latex2 . | 1 |
(Based on P4.15, White) The continuity equation for incompressible flow latex0 expressed in cylindrical polar coordinates latex1 is latex2 What is the most general form of a two-dimensional, purely radial incompressible flow pattern latex3 , latex4 , latex5 that satisfies continuity? | 1 |
*Hint: this proof requires the vector calculus identity* latex1 *where latex2 is the vorticity. | 0 |
A stretch of factor 2 normal to the line latex6 . | 0 |
Show that by combining the inner and outer approximations the general solution in the limit latex31 is recovered. | 1 |
Yes - Input the function No - Type 'none' latex0 latex1 | 0 |
latex12 f(x) latex13 [0,\frac{\pi}{2}] latex14 f(x) latex15 f(x) = \frac{8}{\pi^2}\sum_{n=1,3,5,\ldots}^{\infty} \frac{1}{n^2} (-1)^{(n-1)/2} \sin \left(nx\right) \;, $ and write down the first few terms explicitly. | 1 |
Assume that the suspended soil behaves as a passive scalar that is released instantaneously at the bed and that the flow conditions are those usually encountered for steady uniform open channel flows. | 0 |
A two-stage rocket accelerates in free space by ejecting fuel at a constant relative speed latex0 . | 0 |
What other names are they known by? | 1 |
Assuming that your car can only operate at its limited motor speed, calculated in part b, determine its instanteous acceleration at the beginning of a race (from a standing start). | 1 |
By applying KCL to the circuit below, show that the total resistance of the circuit can be calculated as: latex0 | 1 |
Find the force latex4 . | 1 |
A thermostat switches off the electricity by means of a brass strip, which must be set-up so that it buckles after a temperature rise of latex0 . | 0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.