Q 5: Numerically Solving ODEs with Matlab (25 points) The differential equations governing a Metronomes angular motion ( ) is given by the following second order homogenous differential equation. Where m1 is the mass of body Q1, m2 is the mass of body Q2, k is a torsional spring constant, g is the acceleration due to gravity, and L,h are the given dimensions. 5a) Re-write the differential equation as a system of first order ODEs (do this on paper) Create a script (file name: exam2p5.m ) to: 5b) Solve the initial Value Problem where (0 )= 10 and (0 )=0 / using Matlabs ode45 for (5)= ? Given m1 = 0.1;%kg m2 = 0.02;%kg g = 9.8; %m/s^2 L = 0.2;%m h = 0.1%m k = 2; %N*m/rad 5c) Generate a plot of vs . From your plot determine the number of cycles that have occurred in 5 seconds. Number of cycles = _____________________