Question

A bob of a pendulum swings through an arc of 50 cm on its first swing. Each successive swing is 90% of the length of the previous swing. Find the total distance the bob travels before coming to rest.

Answer 1

Answer:

This is a geometric series problem, with r = 0.99 and a1 = 50 cm.

The sum of a geometric series will give how far it travels:

S = a1 / (1-r)

S = 50 / (1-0.99) = 50/0.01 = 5000 cm = 50 m

Hope this helps!

Answer 2

Given,

The length of the arc$\[ = 50\,{\rm{cm}}\]$

The value of r$\[ = 0.90\]$

Solution,

Formula used, the total distance the bob travels before coming to rest$\[ = \frac{{{a_1}}}{{1 - r}}\]$.

Apply values.

$\[\begin{array}{l} \Rightarrow \frac{{50}}{{1 - 0.90}}\\ \Rightarrow 500\end{array}\]$

Hence,the total distance the bob travels before coming to rest is $\[500\]$cm.