# Simple harmonic motion

1. Nov 3, 2014

### ZARATHUSTRA

• Member warned about posting without the template and with no effort
For one-dimensional simple harmonic motion, the equation of motion, which is a second-order linear ordinary differential equation with constant coefficients, could be obtained by means of Newton's second law and Hooke's law and

i dont get this part which [PLAIN]http://upload.wikimedia.org/math/6/5/6/656fd81e91b7ad38db0c1f263dd5f4af.png[/B] [Broken]

so can somebody explain it to me? Thank you

Last edited by a moderator: May 7, 2017
2. Nov 3, 2014

### vela

Staff Emeritus
What don't you get?

3. Nov 3, 2014

### RUber

The first part is the solution to the differential equation.
The second part is a recast of the solution with one function (cosine).
If you let $\frac{c_2}{c_1}=\tan \phi$ this is the angle sum identity for cosine.

4. Nov 6, 2014

### ZARATHUSTRA

why? why "w'' = the square root of 'k' divided by 'm' i don't get this equation

5. Nov 6, 2014

### vela

Staff Emeritus
Try plugging $x(t) = A\cos(\omega t-\varphi)$ into the differential equation.

6. Nov 12, 2014

### ZARATHUSTRA

how do they people get this equation? , where does it come from? can you show me process of deducting this formula? THANKS!

7. Nov 12, 2014

### vela

Staff Emeritus
Did you try plugging x(t) into the differential equation?

8. Nov 12, 2014

### RUber

It is simply a notational convenience. You could continue to use sqrt(k/m) everywhere but that gets messy.

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