﻿ Work task - Spring Oscillator (Forcced oscillation & Damped oscillation)
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## Spring Oscillator(Forcced oscillation & Damped oscillation)

### Work tasks and measurement procedure

##### Free oscillation
1. Follow the periodic movement of the spring oscillator, record the time dependence and plot it on a graph (select the time period in which it is not too noticeable effect damping).

2. Determine basic harmonic motion parameters from the data waveform instantaneous deflection – the amplitude, the period (frequency) and the initial phase.

3. Determine the amount of weight oscillator knowledge of Spring rigidity (k = 9,85 N/m) – dynamic method of the weight determining.

##### Damped oscillation
1. Follow waveform instantaneous variations in the real (damped) of the oscillator (choose a sufficiently long time interval, in which the effect of sufficiently damping effect).

2. Record the time dependence of the instantaneous displacement damped oscillator and plot it on a graph. Read the decreasing sequence of positive quasi-periodic oscillation maximum deflections.

3. Prove the exponential dependence of the damping of the oscillator obtained data, determine the value of damping coefficient.

##### Forced (excited) oscillation
1. Observe the amplitude of forced oscillation for different excitation frequencies. Approximately estimate the resonance frequency.

2. Record (at least) five sets of temporal variation of elongation forced oscillation at frequencies below the resonant frequency and the estimated (at least) five similar measurements for higher frequencies. Plot the amplitude immediate deflection excitation frequency to a chart (or angular frequency).

3. Determine the resonant frequency of the oscillator from measured data (compare free oscillation frequency, observe the effect of damping).

Note:
The task can only be measured in whole or as individual parts. When used on lower levels of education can reduce the complexity of tasks (eg ignore the influence of damping, etc.).

#### Measuring procedure

1. We run away to the experiment Spring Oscillator (Forcced oscillation & Damped oscillation).

##### Free oscillation
1. We choose the frequency of using ready frequencies or using the slider, so that an immediate course deviation is large enough (you can see in the chart, or on a webcam).

2. We turn off the driving force stop button after setting the required frequency. We will wait a moment until the oscillator goes into free oscillation (to stabilize the oscillation frequency). Then we enable recording of experimental data – Time variation of elongation (record max 5 s).

3. We can shut down the remote experiment (or temporary leave) and go for processing after measuring the required number of data (and the download file experimental values!).

4. We open selected file of experimental data in a spreadsheet.

5. We plot the values of the instantaneous displacement is time to chart. We check the form obtained according to the anticipated harmonic shape.

6. We subtract the amplitude and period of the graph – either classic reading from the graph or using the "fitting" (least squares method) mathematical model of harmonic oscillation – formula (2). In addition to other parameters determine the oscillation and the initial phase of oscillation in the case of working with the mathematical model.

7. We determine the weight of the weight of the obtained period (or frequency) of the formula (3).

##### Damped oscillation
1. We set one of the prepared frequency or use the slider to select the frequency at which the course of the immediate displacement of sufficient size – as in paragraph 2 and 3. Then, turn off the driving force.

2. We start recording of the immediately deflection values after a while, when stabilize the oscillation frequency.

3. We record a longer time interval now to significantly reflected the influence of damping - unlike the previous measurement. We measure thus until the moment when the maximum displacement of the reference oscillation quasi significantly decreases (eg to 20% of its initial value).

4. We can shut down the remote experiment (or temporary leave) and go for processing after measuring the required number of data (and the download file experimental values!)

5. We plot the dependence of the immediate deflection and time to the graph. We check the form obtained according to the expected shape.

6. We subtract the value of gradually decreasing amplitude of the graph (either absolute value or a positive value) – either classic reading on the graph using the "fitting" (least squares method) mathematical model damped oscillation – a formula (4).

7. We draw a graph of the time dependence of the amplitudes obtained. We will test whether this dependence is assumed exponential Using a spreadsheet (Option:*) "Add Trendline… —>Type of trend and regression: Exponential"). We get damping coefficient of the equation obtained dependence (Option:*) "Display the equation in the chart").

##### Forced (excited) oscillation
1. Measurement of this section follows the same pattern as the natural oscillation measurements (see paragraphs from 2 to 4)

2. We perform measurements for at least five lower and higher frequencies than five the natural vibration frequency. Preferably still dopnit by measurements at the resonant frequency (or in close proximity). We try to make the selected frequency as best as possible and evenly covered with the chosen frequency spectrum.

3. We can leave the remote experiment and go for processing after measuring and storing all (at least ten) series of experimental values.

4. We determine the frequency and amplitude of individual cases of forced oscillation – the same paragraphs from 5 to 7.

5. We plot the dependence of the maximum deflection (amplitude) at the excitation frequency graph. Check the shape of the obtained dependence with the expected shape – formula (5).

6. We determine the resonant frequency from the obtained dependence. We compare the result with the value resulting from the previously received parameters – formula (6).

 *) Described dialogs corresponding data processing in MS Excel spreadsheet. In another spreadsheet may be the dialogues wording other (similar), but semantically contain these spreadsheets same functions.