Why is resultant displacement in an composition of simple harmonic motion the sum of individual displacements?

Question

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?

Possible duplicate of Why is the Principle of Superposition true in EM? Does it hold more generally? — Tausif Hossain, Sep 21 '19 at 16:25
Also related: https://physics.stackexchange.com/q/306305/2451 — Qmechanic, Sep 21 '19 at 17:08
I don't think that the duplicate target proposed by @Tausif is a good match for Aman's question. He wants to know why it's physically valid to perform that simple linear combination. — PM 2Ring, Sep 21 '19 at 20:09
@PM2Ring Yes, thats exactly what i want . for me its quite intuitive if the two harmonics are in perpendicular directions . But it poses a problem form me when i think about the composition along the same lime — Aman Sharma, Sep 22 '19 at 05:14

score 0 · Answer 1 · answered Sep 21 '19 at 19:44

0

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...

answered Sep 21 '19 at 19:44

leokruglikov

36

yes do understand the superposition principle if constant forces act on a body. But i fail to understand it when variable forces are acting on that too which are proportional to the displacement from the origin as in the case of SHM. – Aman Sharma Sep 22 '19 at 05:20
But when there is a simple physical pendulum, the force isnt constant either. – leokruglikov Sep 22 '19 at 14:11

Why is resultant displacement in an composition of simple harmonic motion the sum of individual displacements?

1 Answers1