# Homework Help: 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

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.