# Question- LO3 Approximate solutions of contextualised examples with graphical and numerical methods Task 3.0 3.1 (a) The voltage across a capacitor at a time t is given by vc = 120(1 – e-t/CR), where R = 47kΩ and C = 15 uF. Sketch the graph of voltage ag…

LO3 Approximate solutions of contextualised examples with graphical and numerical methods Task 3.0 3.1 (a)The voltage across a capacitor at a time tis given by ye= 120(1 â€” eV), where R= 47kQand C = 15 uf. Sketch the graph of voltage against time and estimate the value of the voltage when t =2s after being connected toa dc supply. (b)Atmospheric pressure p was found to vary with altitude, /as shown in the table opposite Show that this approximately follows the relationship p = ae"and by plotting a suitablearaph, find the constants a and k. Altit Pressure ude 500 73.9 150 0 68.42 300 0 61.6 500 0 53.56, 800 0 43.41

3.2The solution to a differential equation associated with the path taken by a projectile for which the resistance to motion is proportional to the velocity is given by :- Sete *)+x-25 Use (i), the bisection method and (ji) the Newton's method to determine the value of x, correct to 2 decimal places for which the value of y is zero. 3.3An alternating current i has the following values at equal intervals of 5 ms charge.ain coulombs is given by 30x107* a=[ idt o

Deteremine the charge stored in coulombs using (i)the trapezoidal rule an (ii) Simpson's rule. time (ms) | Current(A) 0 0 5 48 10 941 15, 12.7 20 8.8 25, 35 30 0 3.4 (a) The mathematical model of a system is given by the differential equation ®@ = xa+9-p ——(a) Using analytical method the solution of the above differential equation is 2=3t+, ett. Obtain the numerical solution of the differential equation (1)in the range 1.0 (0.2) 2.0 given the initial conditions that at ¢=1, when p =4. When x=1.6, compare the accuracy,correct to 3 decimal places, of the Euler and Euler — Cauchy methods. (b)Critically evaluate the accuracy and the applicability of the above numerical methods.

# Our Happy Testimonials

They are fast in responding to homework questions. they have the best technical writers. Thanks for helping me with my programming doubts.

I contact to disklib for homework, they help me out, despite there was some technical issue they gone through extra mile for me and provide me good quality work in first priority. 100% recommended.

Desklib's study resources are best & unique. Their study database is easy to access and easy to use.

100 % recommended.