We disagree with the exclusion of Newton's laws, Ohm's law and the law of energy conservation from the physics curriculum of elementary schools in the Czech Republic!

Oscillations on the spring
(forced & damped oscillations)

Work Tasks and Measurement Procedures

Work task:

Free Oscillation
  1. Follow the periodic motion of the spring oscillator, record the time dependence and plot it on a graph (choose the time period when the damping effect is not too noticeable).

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

  3. Determine the amount of weight oscillator knowledge of spring stiffness (k = 9,85 N/m) – dynamic method of weight determination.

Damped Oscillation
  1. Follow the waveform instantaneous changes in the real (damped) oscillator (choose a sufficiently long time interval in which the effect of sufficient damping effect).

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

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

Forced (Excited) Oscillation
  1. Observe the amplitude of the forced oscillation for various excitation frequencies. Approximately estimate the resonant frequency.

  2. Record (at least) five sets of time histories of the strain forced oscillation at frequencies below the resonant frequency and estimate (at least) five similar measurements for higher frequencies. Plot the amplitude of the instantaneous deflection excitation frequency on a graph (or angular frequency).

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

The task can only be measured as a whole or in parts. When used at lower levels of training, the complexity of the tasks can be reduced (e.g. ignore the influence of damping, etc.).

Measurement Procedure

  1. We go to the experiment Oscillations on the spring (forced & damped oscillations).

Free Oscillation
  1. We choose the frequency of using the 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. After setting the desired frequency, we turn off the button for stopping the driving force. We wait for a moment until the oscillator goes into free oscillation (to stabilize the oscillation frequency). Then we enable recording of experimental data - time variation of strain (recording max. 5 s).

  3. We can stop the remote experiment (or temporarily leave it) and go for processing after measuring the required number of data (and downloading the file of experimental values!)

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

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

  6. We subtract the amplitude and period of the graph – either classical 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 frequencies or use the slider to select the frequency at which the course of the immediate displacement of sufficient size – as in paragraphs 2 and 3. Then we switch off the driving force.

  2. We start recording the instantaneous displacement values after a while, when the oscillation frequency has stabilized.

  3. We now record a longer time interval to significantly reflect the influence of damping – in contrast to the previous measurement. We measure until the moment when the maximum displacement of the reference oscillation decreases significantly (e.g. 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 download the file experimental values!)

  5. We plot the dependence of the immediate deflection and time on the graph. We check the shape 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 classical 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 obtained amplitudes. We will test whether this dependence is assumed to be exponential using a spreadsheet (Option:*) "Add Trendline… —>Type of trend and regression: Exponential"). We obtain the damping coefficient of the equation obtained dependence (Option:*) "Display the equation in the chart").

Forced (Excited) Oscillation
  1. The measurement of this section follows the same pattern as the measurement of natural vibration (see paragraphs 2 to 4).

  2. We make measurements for at least five frequencies lower and higher than the natural frequency. Preferably, we make measurements at the resonance frequency (or close to it). We try to make the chosen frequency as good 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. Plot the dependence of the maximum deflection (amplitude) on the excitation frequency. Check the shape of the obtained dependence with the expected shape – formula (5).

  6. Determine the resonance frequency from the obtained dependence. Compare the result with the value resulting from the previously obtained parameters – formula (6).

*)  Described dialogs correspond to data processing in MS Excel spreadsheet. In another spreadsheet the dialogs may have different (similar) wording, but semantically these spreadsheets contain the same functions.