Presentation showcase | PresentStudio

Back to showcaseScientific · The Simple PendulumMake your own

Scientific · The Simple PendulumRevision 1 · 5 slides

two column

The Simple Pendulum: From Motion to Measurement

What sets the rhythm of a pendulum?

Oscillation: one complete back-and-forth cycle. Period T: time per cycle (s).

⌣

pivot

L (m)

bob

g (m/s²)

PENDULUM / 01

The small-angle model

Length sets the ideal period

T = 2π √(L/g)

T: period (s) L: pivot-to-bob-center length (m) g: 9.81 m/s²

4× length → 2× period

Mass is absent from this ideal formula.

Assumptions: point-mass bob; massless, fixed-length string; negligible drag and pivot friction; initial angle ≲10°.

PENDULUM / 02

Calculated predictions

Longer means slower—not in direct proportion

Rows: length L (m)

0.25

1.003

0.5

1.419

0.75

1.737

2.006

1.5

2.457

2.837

Horizontal: period T (s)

0.25 m → 1.003 s 0.5 m → 1.419 s 0.75 m → 1.737 s 1 m → 2.006 s 1.5 m → 2.457 s 2 m → 2.837 s

Equal length increases produce smaller period increases.

Calculated values; not measurements.

Categorical spacing; unequal L intervals.

PENDULUM / 03

two column

Square the period to reveal linearity

T² = (4π²/g)L

Theoretical slope 4.024 s²/m

g = 4π²/slope ≈ 9.81 m/s²

Calculated ideal-model values; not experimental measurements.

An experimental slope can test this model.

Rows: L (m) · bar values: T² (s²)

0.25

1.006

0.5

2.012

0.75

3.018

4.024

1.5

6.036

8.049

process

From model to an independent measurement

Measure → release

Pivot-to-bob-center L Small angle; no push

Time → divide

20 full oscillations T = total time / 20

Repeat → compare

Repeat at each L Plot measured T² against L

Limits: timing uncertainty · length uncertainty · damping · larger angles

Longer pendulums swing more slowly; linearization connects motion to gravity.

Opening the presentation…

Scientific · The Simple PendulumRevision 1 · 5 slides

two column

The Simple Pendulum: From Motion to Measurement

What sets the rhythm of a pendulum?

Oscillation: one complete back-and-forth cycle. Period T: time per cycle (s).

⌣

pivot

L (m)

bob

g (m/s²)

PENDULUM / 01

The small-angle model

Length sets the ideal period

T = 2π √(L/g)

T: period (s) L: pivot-to-bob-center length (m) g: 9.81 m/s²

4× length → 2× period

Mass is absent from this ideal formula.

Assumptions: point-mass bob; massless, fixed-length string; negligible drag and pivot friction; initial angle ≲10°.

PENDULUM / 02

Calculated predictions

Longer means slower—not in direct proportion

Rows: length L (m)

0.25

1.003

0.5

1.419

0.75

1.737

2.006

1.5

2.457

2.837

Horizontal: period T (s)

0.25 m → 1.003 s 0.5 m → 1.419 s 0.75 m → 1.737 s 1 m → 2.006 s 1.5 m → 2.457 s 2 m → 2.837 s

Equal length increases produce smaller period increases.

Calculated values; not measurements.

Categorical spacing; unequal L intervals.

PENDULUM / 03

two column

Square the period to reveal linearity

T² = (4π²/g)L

Theoretical slope 4.024 s²/m

g = 4π²/slope ≈ 9.81 m/s²

Calculated ideal-model values; not experimental measurements.

An experimental slope can test this model.

Rows: L (m) · bar values: T² (s²)

0.25

1.006

0.5

2.012

0.75

3.018

4.024

1.5

6.036

8.049

process

From model to an independent measurement

Measure → release

Pivot-to-bob-center L Small angle; no push

Time → divide

20 full oscillations T = total time / 20

Repeat → compare

Repeat at each L Plot measured T² against L

Limits: timing uncertainty · length uncertainty · damping · larger angles

Longer pendulums swing more slowly; linearization connects motion to gravity.