# Problem I. 162. (May 2007)

**I. 162.** Prepare a sheet to simulate the damped oscillation of a mass attached to a spring in one dimension and to calculate the frequency of the oscillation.

The first four rows of the sheet contain the mass of the body (*m*), the spring constant (*D*), the damping factor (*k*) and the time steps used in the simulation. The first four columns in the following lines then should contain the elapsed time, the amplitude, the velocity and the acceleration of the body, corresponding to a simulation step. The duration of the simulation should be long enough. The frequency of oscillation should be printed in the fourth column of the first line, according to the simulation. Your sheet should also contain a graph showing the amplitude, the velocity and the acceleration of the body as functions of time.

You should compute the instantaneous acceleration in every simulation step, and then derive the instantaneous velocity and amplitude from this. The instantaneous resultant force acting on the body is *F*=-*D*^{.}*x*-*k*^{.}*v*, where *x* is the amplitude and *v* is the velocity.

The sheet (`i162.xls`, ...) is to be submitted.

(10 pont)

**Deadline expired on June 15, 2007.**

Sorry, the solution is available only in Hungarian. Google translation

A feladat mintamegoldása: i162minta.xls

### Statistics:

11 students sent a solution. 10 points: Balambér Dávid, Danka Miklós András, Gilián Zoltán, Györök Péter, Szoldatics András, Vincze János. 8 points: 2 students. 4 points: 1 student. 2 points: 1 student. 1 point: 1 student.

Problems in Information Technology of KöMaL, May 2007