14167 Experiment Pack - Mechanics in Physics - info

M2: 1                OSCILLATION PERIOD OF A SIMPLE  PENDULUM

 (n.b. all worksheets have diagrams of experimental set-up)

Material

1 Stand rail 30 cm

1 Rod 25 cm

1 Rod 50 cm

1 Table clamp SE

2 Universal bossheads SE

1 Round bosshead

1 Masshanger

4 Slotted masses 50 g

1 Bearing pin

1 Measuring tape

1 Pair of scissors

String

 Additional material recommended: 1 Stop-watch

 Investigation

To investigate the oscillation period of a simple pendulum.

Preparation

Arrange according to the illustration. The table clamp with stand rail is attached to the edge of the table. The 50 cm rod is clamped vertically in the stand rail. First the lower universal bosshead is fixed to the rod in a parallel position to the edge of the table. It should touch the stand rail. The rod is lengthened by attaching the 25 cm rod by means of the round bosshead.

The upper universal bosshead is clamped in such a way that it points to the front. The bearing pin is clamped in the upper universal bosshead so that it projects over the edge of the table as far as possible.

The masshanger is attached to a piece of string of about 1 m. The other end of the string is tied with a loop and led through the drill hole of the bearing pin. The string is hung into the knurled screw of the lower universal bosshead.

By shifting this universal bosshead the length of the pendulum can be adjusted. The length of the pendulum is the distance from the bearing pin to the centre of gravity of the attached mass.

Experiment 1

Two 50 g slotted masses are placed on the masshanger. The length of the pendulum I is adjusted to 40 cm. The pendulum is moved about 5 cm from its neutral position and it starts swinging. The period of time for 10 oscillations (one oscillation consists of a movement to and fro) and therefore the duration T for one oscillation is determined.

          Period of time for 10 oscillations:          ........ s

          Duration T:                                ........ s

Experiment 2

The pendulum is again moved from its neutral position, about 10 cm. The period of time for 10 oscillations is measured and therefrom the duration T for one oscillation determined.

          Period of time for 10 oscillations:          ......... s

          Duration:                                   ......... s

The period of oscillation is the same as in the first experiment. The dislocation from the neutral position does not matter as long as it is small.

Experiment 3

Four 50 g slotted masses are put on the masshanger. The length of the pendulum remains 40 cm, but the length of the string must be corrected because of the dislocation of the centre of gravity (move the lower universal bosshead). The centre of gravity is now approximately between the second and third slotted mass.

The period of time for 10 oscillations is measured and therefrom the duration for one oscillation determined.

          Period of time for 10 oscillations:          ........ s

          Duration T:                                ........ s

The period of oscillation is the same as in the first experiment, this proves that it does not depend on the mass.

 Experiment 4

The length of the pendulum is shortened to 0,25 m, i.e. half its original length (therefore a second loop must be tied in the string). Only one slotted mass 50 g is put on the masshanger.

          Period of time for 10 oscillations:          ........ s

          Duration T:                                ........ s

Experiment 5

The pendulum is lengthened to 80 cm.

          Period of time for 10 oscillations:          ........ s

          Duration T:                                ........ s

If the length of the pendulum is four times larger, the duration of the oscillation is twice as long.

Conclusions

The duration (or period), T, of an oscillation of a simple pendulum does not depend on the displacement from its neutral position. Nor does it depend on the weight of the pendulum.

If the length, L, of the pendulum doubles the duration of the oscillation lengthens by about 1.4 times.

The results of the experiments are compared to the formula

          T  =  2p Ö  L/g    where g = acceleration due to gravity

(This is an approximation – it is not true for very large swings.)