Find the sum of two harmonic motions of equal amplitude but of slightly differen

Question

Find the sum of two harmonic motions of equal amplitude but of slightly different frequencies. Discuss the beating phenomena that result from this sum. A mass is subjected to two harmonic motions given by y1(t) = Y cos omega1 t and y2(t) = Y cos omega2 t in which Y = 0.40", omega1 = 25 rad/s and omega2 = 26.25 rad/s. Plot the resulting motion of the mass (you may use any software available to you); Determine the beat frequency. Solve the same problem when Y = 10 mm while all other information remains unchanged.

Explanation / Answer

x1= 0 + i sin(9t-0.5) x2 = cos(8t+1.5) + 0.0i x1+x2 = cos(8t+1.5) + 0.0i 0 + i sin(9t-0.5) =[cos(8t+1.5) + 0]+[ 0.0i + i sin(9t-0.5)] = cos(8t+1.5) + i sin(9t-0.5) ? the sum of two simple harmonic motions x1+x2 = cos(8t+1.5) + i sin(9t-0.5)

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