Find the formula for the general solution to the harmonic oscillator that is gov

Question

Find the formula for the general solution to the harmonic oscillator that is governed by the equation d2x/dt2 = (-1/6)x (k = 1 and m= 6)

USE MATLAB code

(b) Find the solution that satisfies the conditions x(0) = 4.1 and x' (0) = 6.5

Create a plot of the solution. Notice the slope of the curve at t = 0 ... it should be 6.5.

(c) Use Manipulate to plot the solution to the differential equation in (a) with a damping term added. If c is the damping constant, determine the smallest value of c for which the solution never becomes negative.

Explanation / Answer

slopes.m

function dxdt = slopes(t, x)
dxdt = [x(2); -1*x(1)/6];

script.m

[t x] = ode23(@slopes, [0 10], [4.1; 6.5]);
plot(t, x(:,1));

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.