Author: Anonymous

ANSWER ON A CLEAN SHEET OF WHITE PAPER. Problem 4:  How would you modify the conditions for the following reaction to provide the cis product only? (3 points)  

37. The development of the Megaron form is attributed to which civilization?

ISIQEPHU A: ISIFUNDO SOKUQONDISISA UMBUZO 1: Fundisisa lesi siqephu esingezansi bese uphendula imibuzo ezolandela. Read the comprehension below and answer the questions that follow.   CLICK ON THE BUTTON BELOW TO SEE THE TEXT:

1.1.8 Bhala le gama ngesiNgisi: Amalungelo Write this word in English: Amalungelo   (2)

2.7 Gugqula le misho ube senkathi ezayo eqhubekayo: Change these sentences into a future continuous tense:  a) Umama upheka iphalishi elimnandi.       (Mother is cooking nice porridge.)  b) Ubaba ushayela ibhasi.        (Father drives a bus.)   (4)

2.4. Qondanisa isandiso  nohlobo lwesandiso oluhambelana nalo. Match an adverb with a type of adverb that represent it.   (4)

1.1.6 Yebo noma Cha: USphihli yinkomo yesifazane? True or false: Sphihli is a female cow? (2)

ISIQEPHU B: UKUSETSHENZISWA KOLIMI UMBUZO 2 2.1 Khetha ibizomfakela kulawa alandelayo. Choose a borrowed noun from the following nouns. (2)

Problem 4 (25 points) Consider the following initial value problem associated with the response of a nonlinear spring written in non-dimensional state-space form:                         du / dt = v                         dv / dt = -ω2 ( 1 + ( u / ubar )2 )                                                                          with ω = 1 and ubar = 2 The initial conditions are specified as u(0) = 1 and v(0) = -1 Perform the first two steps of a second order Runge-Kutta method with a step size of Δt = 0.10 to determine approximate solutions at time t = 0.20 Note: This step size is only for illustrative purposes. In practice, a much smaller Δt  would be selected.

Problem 3 (25 points) For each case defined below, write a sample ordinary differential equation (ode), along with any required additional conditions. Include the identification of the independent and dependent variables. An initial value problem defined by a second order linear homogeneous ode with constant coefficients having a non-trivial solution. A boundary value problem involving a fourth order linear nonhomogeneous ode. A first order homogeneous nonlinear ode.