(20 pts.) Show numerically the validity of the following expression 178 V where

Question

(20 pts.) Show numerically the validity of the following expression 178 V where Hint: use the Matlab intrinsic functions sin and sqrt and the built-in Matlab constant pi. (25 pts.) The acceleration of a reciprocating engine piston is given by1 (r-sin2 ?)32 where n-lr, r is the crank arm length, l is the length of the connecting rod, co is the angular velocity of the crank arm, and ? is the rotation angle of the crank arm. Write a Matlab code that takes n and ? as inputs and display the value of the ratio a/(??2) on the screen. Test your code for n-3 and 6-pi/7

Explanation / Answer

1) To check the validity of the expression, we need to check whether LHS is equal to RHS

seperate expressins are written and LHS and RHS and their results are displayed seperately

clear all;close all;clc;commandwindow;
gamma_square=17-sqrt(17);
gamma=sqrt(gamma_square);
alpha=sqrt(34+(sqrt(2)*(sqrt(17)-1)*gamma)-(8*sqrt(2)*sqrt(sqrt(17)+17))+(6*sqrt(17)));
RHS=(sqrt(2)/8)*(sqrt(gamma_square-(sqrt(2)*(alpha+gamma))));
LHS=sin (pi/17);

display(LHS)
display(RHS)

OUTPUT

LHS=

0.1837

RHS=

0.1837

2)

theta=input('enter the value of theta');
n=input('enter the value of n');
arw=cos(theta)+(((n.^2)*cos(2*theta)+sin(theta).^4))/(((n.^2)-sin(theta).^2).^(3/2))

OUTPUT

enter the value of theta

pi/7

enter the value of n

3

arw=

1.1168

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