Error Propagation: Dividing By 20 in Pendulum Timing

[PhysicStud01]

Homework Statement

suppose i measure the time t for 20 oscillations fro a pendulum. the period is T.

Homework Equations

Since T = t / 20
delta T = delta t right?

The Attempt at a Solution

since the 20 is a numerical value, it does not come in the error propagation, does not? when i used the above equation, i can't get the required answer but when i divide by 20, the answer is obtained.

can someone explain why?

 

[Nathanael]

T is what you measure the period to be, right? (T = t / 20) So the true period will be T+ΔT where ΔT is some error.

The true time it takes for 20 oscillations is 20(T+ΔT), which equals the time you measured plus some error Δt

$20(T+ΔT)=t+Δt$

So if $20T=t$ then:

$20ΔT=Δt$ ... or ... $ΔT=\frac{Δt}{20}$