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Chapter 13: Problem 29

At the heart of a grandfather clock is a simple pendulum \(1.45 \mathrm{m}\) long; the clock ticks each time the pendulum reaches its maximum displacement in either direction. What's the time interval between ticks?

Short Answer

Expert verified
The time interval between each tick of the clock is approximately \(2.42 \, s\).

Step by step solution

01

Identify Given Parameters

The length of the pendulum, \(l\), in the clock is given as \(1.45 \, m\). The acceleration due to gravity, \(g\), is approximately \(9.8 \, m/s^2\). These are the two parameters we will use to calculate the time interval between ticks.
02

Apply the formula for the period of a pendulum

We use the formula for the period of a simple pendulum, \(T = 2\pi\sqrt{\frac{l}{g}}\). Substituting the given values we get \(T = 2\pi\sqrt{\frac{1.45}{9.8}}\).
03

Compute the Time Interval

After calculating the above expression, we obtain the period of pendulum which is also the time interval between each tick.

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