Harmonic Oscillator with random number-mathlab

[Api]

Hello there,
lets say i have a harmonic oscillator equation d^2x/dt^2 = -w^2 x = -Asin(wt)
w=frequency, A=amplitude..how can i plot this equation for w^2=1, x(0)=1?

and what if the equation contains random number d^2x/dt^2 = -w^2x+Bn, n=gaussian random number with mean value equal to zero. Under the same condition, how do i plot this for 1 trajectory solution (1 time only) and step=0.1?

I m very new to mathlab and i really need to learn these basics to solve the real problem in my project...any help will be very much appreciated..thanks.

 

[NateD]

To plot the harmonic oscillator equation in MATLAB, you can use the following commands: %Define the constantsw = 1;A = 1;%Define the initial conditionsx0 = 1;x_dot0 = 0;%Define the time vectort = 0:0.1:10;%Solve the ODE using ode45[t,x] = ode45(@(t,x) [-w^2*x;x_dot0],t,x0);%Plot the solutionplot(t,x,'r')xlabel('Time (s)')ylabel('Position (m)')title('Harmonic Oscillator')For the equation with a random number, you can use the same approach but with a slightly different function definition. You need to define a function that takes the current time and position as inputs and generates a random number for the B coefficient. Here is an example of how this could be done:%Define the constantsw = 1;A = 1;B = 1;%Define the initial conditionsx0 = 1;x_dot0 = 0;%Define the time vectort = 0:0.1:10;%Define a random number generatorrandn('state',sum(100*clock));%Define the ODE functionfunction x_dot = harmonic_oscillator(t,x) n = randn; x_dot(1) = -w^2*x + B*n; x_dot(2) = x_dot0;end%Solve the ODE using ode45[t,x] = ode45(@harmonic_oscillator,t,x0);%Plot the solutionplot(t,x,'r')xlabel('Time (s)')ylabel('Position (m)')title('Harmonic Oscillator with Random Noise')