Question

A simple pendulum takes 2.00 s to make one compete swing. If we now triple the length, how long will it take for one complete swing

Answer 1

Answer:

3.464 seconds.

Explanation:

We know that we can write the period (the time for a complete swing) of a pendulum as:

$T = 2*\pi*\sqrt{\frac{L}{g} }$

Where:

$\pi = 3.14$

L is the length of the pendulum

g is the gravitational acceleration:

g = 9.8m/s^2

We know that the original period is of 2.00 s, then:

T = 2.00s

We can solve that for L, the original length:

$2.00s = 2*3.14*\sqrt{\frac{L}{9.8m/s^2} }\\\\\frac{2s}{2*3.14} = \sqrt{\frac{L}{9.8m/s^2}}\\\\(\frac{2s}{2*3.14})^2*9.8m/s^2 = L = 0.994m$

So if we triple the length of the pendulum, we will have:

L' = 3*0.994m = 2.982m

The new period will be:

$T = 2*3.14*\sqrt{\frac{2.982m}{9.8 m/s^2} } = 3.464s$

The new period will be 3.464 seconds.