How does the period of a pendulum affect its time measurement?

[DorelXD]

Homework Statement

A pendulum clock measures the time exactly if its period is $T_0$. What time does the pendulum record in a time $D$ , if its period becomes $T$ ?

Homework Equations

I know that the number of oscilations of the pendulum in the time D is : N=D/T

The Attempt at a Solution

Well I don't know how to use the informations that the probelm gives me.
P.S. : SORRY FOR THE SPELLING IN THE TITLE

 

[mfb]

Each period of the pendulum, the display of the clock goes forwards by T₀.
After N periods, what does the clock show?

 

[DorelXD]

Each period of the pendulum, the display of the clock goes forwards by T₀.
After N periods, what does the clock show?

Ohhhhh I get it now. I looked more closely in the mechanism of the pendulum. From what I understood, each time an oscillation is completed the pendulum records a certain time. Let this time be $t$. This $t$ is constant, and its typical for every pendulum, right ?

In our problem the period , i.e. the time needed for an oscillation to be completed , is modified. But, because our $t$ is a constat, the pendulum will record the same time for each oscilation, even if the number of oscilations increases or decreases.

In our problem:

In a time D, the pendulum swings : $N=\frac{D}{T}$ times => the pendulum measures the time $Nt$ .

Who is $t$ ? Well we know, from the hypothesis that $\frac{D}{T_0}t=D$, that is , if the period is $T_0$ then the time measured by the pendulum is D. Solving for t, we obtain: $t = T_0$ .

So, $Nt = NT_0=\frac{D}{T}T_0$. This is the time the pendulum measures.

Please, help me, and tell me if my judgement is correct. I believe that what confused me before was that I wasn't fully aware that the mechanism of a pendulum allows it to record the same amount of time, and that this time ( $t$ ) doesn't depend on the number of oscilations.

 

[mfb]

Ohhhhh I get it now. I looked more closely in the mechanism of the pendulum. From what I understood, each time an oscillation is completed the pendulum records a certain time. Let this time be $t$. This $t$ is constant, and its typical for every pendulum, right ?

In our problem the period , i.e. the time needed for an oscillation to be completed , is modified. But, because our $t$ is a constat, the pendulum will record the same time for each oscilation, even if the number of oscilations increases or decreases.

Right.

In our problem:

In a time D, the pendulum swings : $N=\frac{D}{T}$ times => the pendulum measures the time $Nt$ .

Who is $t$ ? Well we know, from the hypothesis that $\frac{D}{T_0}t=D$, that is , if the period is $T_0$ then the time measured by the pendulum is D. Solving for t, we obtain: $t = T_0$ .

So, $Nt = NT_0=\frac{D}{T}T_0$. This is the time the pendulum measures.

Correct.

 

[DorelXD]

Thank you very much!