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I recently came across the concept of the composition in simple harmonic motion. A paragraph says that: If

$$x_1 = A_1sin(\omega t)$$

$$x_2 = A_1sin(\omega t + \phi)$$

Then, the resultant displacement is $x_1 + x_2$

But what is exactly happening in this case that we are adding these positions? Are we assuming that the particle is initially and origin and forces f1 and f2 act on the body which cause the SHMs?

Aman Sharma
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2 Answers2

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For me this is quite intuitive... this is the superposition principle for coordinates. If you derive both sides, you will get an expression of v(t), that is also true to the superposition principle. Remember that oscillation or harmonic motion is also a motion therefore obey the principle of superpositon...

leokruglikov
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These two equations are SHM of the same body which started to oscillate after sometime(phase difference). well we can look at these equations in force form by differentiating the equations twice we get there accelerations as a function of x then we know that if a body has two forces F1 and F2 acting on it then applying Newton's second law then at force is body mass times acceleration so now if we integrate twice to find the position vector of the body it will be the simple algebraic sum of those two given position vector. Hence superposition holds true here .

Kaustoobh
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