Question

The time period, T, of a simple pendulum is directly proportional to the square root of the length, d, of the pendulum.

Answer 1

Answer:

$T = 3.54$

Step-by-step explanation:

Given

Direct Variation of T to $\sqrt d$

$d =6;\ when\ T = 5$

Required

Determine T when d = 3

The variation can be represented as:

$T\ \alpha\ \sqrt d$

Convert to equation

$T = k\sqrt d$

$d =6;\ when\ T = 5$; so we have:

$5 = k * \sqrt 6$

Make k the subject:

$k = \frac{5}{\sqrt 6}$

To solve for T when d = 3.

Substitute 3 for d and $k = \frac{5}{\sqrt 6}$ in $T = k\sqrt d$

$T = \frac{5}{\sqrt 6} * \sqrt{3}$

$T = \frac{5\sqrt{3}}{\sqrt 6}$

$T = \frac{5 * 1.7321}{2.4495}$

$T = \frac{8.6605}{2.4495}$

$T = 3.5356$

$T = 3.54$ -- approximated