Error in the time period of a pendulum
T = 2 π √(l/g). T is the time period, l the length and g the acceleration due to gravity.
Error in a formula
Maximum error in T
0.75%
- l1/20.5 × 1%0.5%
- g1/20.5 × 0.5%0.25%
- Totaladd them0.75%
Product, quotient or power: the percentage errors add, each counted |power| times.
0.75% maximum error in T
ΔT/T × 100 = 0.5 × Δl/l × 100 + 0.5 × Δg/g × 100
Product, quotient or power: the percentage errors add, each counted |power| times. A square root is a power of 1/2, so each error counts half.
Other formulas
Measured the same thing several times? Use repeated readings, or find the least count of your instrument.
Error in the time period of a pendulum: quick answers
What is the formula for the error in the time period of a pendulum?
T is the time period, l the length and g the acceleration due to gravity. With T = 2 π √(l/g), the maximum error is given by ΔT/T × 100 = 0.5 × Δl/l × 100 + 0.5 × Δg/g × 100. Product, quotient or power: the percentage errors add, each counted |power| times.
How do I work out the error with real numbers?
Take l with 1% error and g with 0.5% error. The maximum percentage error in T is 0.5 × 1% + 0.5 × 0.5% = 0.75%.
Why are the errors added and never subtracted?
The error shown is the largest possible one. In the worst case every measurement is off in the direction that pushes the result the same way, so the errors pile up. They are added even when the quantity is divided or subtracted.