# Forced harmonic motion

1. Account for any discrepancy between the theoretical and measured values of f.

(f = natural frequency of spring-mass system)

(theoretical: 0.981Hz ; measured: 0.927Hz)

2. Comments on the forced oscillation of the spring-mass system as shown by the s-t graphs obtained.

(in total 3 graphs, with driving frequency lower than, higher than and nearly equal to the natural frequency of the system)

3. Think if there is any further investigations of forced oscillation of the spring-mass system.

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Since you did not give a description of your experiment, I could only give general answers applicable to a forced oscillation system.

1. The main discrepancy is because of the effective mass of the spring, as part of the spring also oscillates. This would effectively increase the oscillating mass and lead to an increase in the period of oscillation. Thus, the measured frequency is somewhat lower than the theoretical frequency.

2. Since these three graphs are not shown, I suggest you could comment on the amplitude of oscillation. The one with driving frequency that is nearly equal to the natural frequency should give large amplitude.

3. You could investigate the phase difference between the driving force and the displacement of the oscillating mass. You would notice that there is a phase change from zero to pi phase difference when the frequencies of the driving force increases. At resonance (i.e. driving frequency equals to natural frequency), the phase change is pi/2 radians.