Answer Happy

3. Using ONLY MATLAB or OCTAVE as your programming platform,
i) Explain the algorithm you will apply in your programming
platform to implement the chosen numerical method from Question 2.
(NO code is required for this question).
ii) Develop a flowchart based on your algorithm and explain the
flowchart. (NO code required for this question. .
iii) Given that 𝐸 = 69 𝐺𝑃𝑎, 𝑡 = 0.1 𝑐𝑚, 𝜌 = 2700 𝑘𝑔𝑚−3 , 𝐿 = 20
𝑐𝑚. Develop a SINGLE script of code in your programming platform to
solve for 𝛽𝑛 AND calculate the fundamental natural frequency of the
beam, 𝜔1, in Hz to four decimal places. For your initial guess use
any values between 0 and 2. For your stopping criteria, stop the
iteration when 𝜀 ≤ 0.01. Also, assume that 𝛽𝑛 = 𝛽1. (Please fully
comment your code and display the output of your code in table form
as shown in lecture. Paste your code inside the report. DO NOT
screenshot your code for the report. Make sure that your code
reflects the flowchart, algorithm and steps that you have
given)
The fundamental natural frequency of a cantilever beam is determined by the following equation: W1 = Et2 V 12p24 、 (1) 217 where w1 is the fundamental natural frequency of the beam in Hz, E is the beam Young's modulus, t is the thickness of the beam, p is the beam's density, L is the length of the beam and B1 is the fundamental eigenfrequency of the beam which can be determined as the smallest absolute value from the characteristic equation of the following matrix in equation (2). In equation (2), n correspond to the vibration mode number. cosh(Ⓡn) sinh(Bn) + sin (Bn) (2) sinh(B) - sin (87) cosh(Pn) [4] = [since