Using matlab solve:
2. If we now assume the mass in equation (2) is initially at rest and has no initial displacement, that is y(0)- y(0) 0, show that the solution in (3) becomes (cos(wt) cos(urot)) y(t) (4) Next use the trigonometric identity 2 sin sin cos (0- cos(0 p) to convert (4) to 2Fo (wo-w)t y(t) (5) Sun Sun In this equation if we let the circular frequency of the driving force be approxi- mately equal to the natural circular frequency of the mass-spring system, that is w wo, we encounter a phenomenon called beats. The factor sin (wo w)t oscillates much faster than sin a so equation (5) describes a rapidly (wo w) oscillating function with circular frequency oscillating inside a slower sinusoidal function. The faster oscillating function has 2Fo (wo w)t Sinusoidal Amplitude (6) m (wa-w2) and period When beats occur we say that the faster oscillating wave wo w is amplitude modulated by the slower varying wave. The slower wave has and period What I would like you to do is to amplitude create a script file in MATLAB that will generate a single graph containing the curve described in equation (5) and also the curves 2Fo (wo Sin m (wa-wa) using the values w 1, wo 1.1, Fo 0.5 and m 0.3. Be sure to include one full period of the slower varying wave and also label your axes and title the graph. Your result should resemble the image below. 2. If we now assume the mass in equation (2) is initially at rest and has no initial displacement, that is y(0)- y(0) 0, show that the solution in (3) becomes (cos(wt) cos(urot)) y(t) (4) Next use the trigonometric identity 2 sin sin cos (0- cos(0 p) to convert (4) to 2Fo (wo-w)t y(t) (5) Sun Sun In this equation if we let the circular frequency of the driving force be approxi- mately equal to the natural circular frequency of the mass-spring system, that is w wo, we encounter a phenomenon called beats. The factor sin (wo w)t oscillates much faster than sin a so equation (5) describes a rapidly (wo w) oscillating function with circular frequency oscillating inside a slower sinusoidal function. The faster oscillating function has 2Fo (wo w)t Sinusoidal Amplitude (6) m (wa-w2) and period When beats occur we say that the faster oscillating wave wo w is amplitude modulated by the slower varying wave. The slower wave has and period What I would like you to do is to amplitude create a script file in MATLAB that will generate a single graph containing the curve described in equation (5) and also the curves 2Fo (wo Sin m (wa-wa) using the values w 1, wo 1.1, Fo 0.5 and m 0.3. Be sure to include one full period of the slower varying wave and also label your axes and title the graph. Your result should resemble the image below
