Search - Numbas at mathcentre.ac.uk

28 results.

GEMIDDELD: Valbeweging van een balletje
Draft
Question in Panamaconferentie by Alexander Holvoet and 1 other

1) Schrijf een modeloplossing. Houd rekening dat je bij randomisatie dit anders zal moeten schrijven.

2) Randomiseer de snelheid, en controleer welke effecten dat heeft op de andere variabelen.
Numbas demo: Motion under gravity
Ready to use
Question in Demos by Christian Lawson-Perfect

Customised for the Numbas demo exam

Motion under gravity. Object is projected vertically with initial velocity $V\;m/s$ . Find time to maximum height and the maximum height. Now includes an interactive plot.
Transfer function from differential equation
Ready to use
Question in IE303412 Cybernetics by Aleksander Skrede and 1 other

This question tests the students skill on transfer functions and Laplace of differential equations. The coefficients of the functions are created randomly.
Julie's copy of Second order differential equations 1
Draft
Question in Julie's workspace by Julie Crowley

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$ .

rebelmaths
Julie's copy of Second order differential equations 2
Draft
Question in Julie's workspace by Julie Crowley

Method of undermined coefficients:

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$ . (Equal roots example). Includes an interactive plot.

rebelmaths
First order differential equations 8
Ready to use
Question in Bill's workspace by Bill Foster

Solve for $x(t)$ , $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$
Dynamical system 9: Saddle.
Ready to use
Question in Bill's workspace by Bill Foster

Asking users to input coefficients of a system of diff equations so that the phase space is a saddle. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$
Dynamical system 7: Stable spiral.
Ready to use
Question in Bill's workspace by Bill Foster

Asking users to input coefficients of a system of diff equations so that the phase space is a stable spiral. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$
Dynamical system 6:Centre.
Draft
Question in Bill's workspace by Bill Foster

Asking users to input coefficients of a system of diff equations so that the phase space is a centre. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$
Bill's copy of Dynamical system 6:Centre.
Ready to use
Question in Bill's workspace by Bill Foster

Asking users to input coefficients of a system of diff equations so that the phase space is a centre. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$
Dynamical system 4
Ready to use
Question in Bill's workspace by Bill Foster

Nature of fixed points of a 2D dynamical system.

These examples are either centres or spirals.
Hyperbolic Functions 2
Draft
Question in Bill's workspace by Bill Foster

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Chain rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Differentiate products of trig, log and exponential terms
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Differentiate products of hyperbolic functions
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Chain rule - hyperbolic and log functions
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Solve a second order ODE with repeated roots,
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$ . (Equal roots example).
Limiting speed given acceleration function,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

An object moves in a straight line, acceleration given by:

$\displaystyle f(t)=\frac{a}{(1+bt)^n}$ . The object starts from rest. Find its maximum speed.
Separable first order ODE with boundary condition
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x(t)$ , $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$
Second order ODE with constant coefficients and boundary conditions
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$ .
Differential Equation Question Type
Draft
Question in Andrew's workspace by Andrew Iskauskas

Solving a second-order constant coefficient ODE. Uses the differentiation extension: https://github.com/Tandethsquire/Differentiation, and the Differential Equation custom part type, to differentiate a student answer and ensure it satisfies the equation.
Solution curves and Vector fields 1 : dy/dx=sin(x-y)
Ready to use
Question in Bill's workspace by Bill Foster

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=\sin(x-y)$ , and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of $f(x,y)$ and that of the variable str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$ .
Solution curves and Vector fields 2 : $dy/dx=x^2-y^2$
Ready to use
Question in Bill's workspace by Bill Foster

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^2-y^2$ , and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of $f(x,y)$ and that of the variable str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$ .
Julie's copy of Second order differential equations 5
Draft
Question in Julie's workspace by Julie Crowley

Find the general solution of $y''+2py'+(p^2-q^2)y=x$ in the form $Ae^{ax}+Be^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral.

rebelmaths
Julie's copy of First order differential equations 5
Draft
Question in Julie's workspace by Julie Crowley

Find the solution of $\displaystyle x\frac{dy}{dx}+ay=bx^n,\;\;y(1)=c$

rebelmaths
Julie's copy of First order differential equations 4
Draft
Question in Julie's workspace by Julie Crowley

Find the solution of $\displaystyle \frac{dy}{dx}=\frac{1+y^2}{a+bx}$ which satisfies $y(1)=c$

rebelmaths
Julie's copy of First order differential equations 1
Draft
Question in Julie's workspace by Julie Crowley

Solve 4 first order differential equations of two types: $\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

rebelmaths
Second order differential equations - sine forcing
Ready to use
Question in Daniel's workspace by Daniel Nucinkis

Find the general solution of $y''+2py'+(p^2-q^2)y=A\sin(fx)$ in the form $A_1e^{ax}+B_1e^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral. Use initial conditions to find $A_1,B_1$ .

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