Question

Find the distance traveled in one back-and-forth swing by the weight of a 12 in. Pendulum that swings through a 75 degree angle.

Answer 1

The distance traveled by pendulum, in one back-and-forth swing is 75.75 inches.

The period of pendulum can be calculated by

$T = 2\pi \sqrt {\dfrac Lg}$

Where,

$T$ - period

$L$ - length = 12 inches

$g$- gravitational acceleration  = $\bold {9.8\rm \ m/s^2}$

Put the values,

$T = 2\pi \sqrt {\dfrac {12}{9.8}}\\\\T = 2 \times 3.14 \times \sqrt {0.122}\\\\T = 2.191$

Now, the angular displacement of the pendulum can be calculated by,

$\theta = A\times\rm \ cos(\omega T)$

Where,

$A$- amplitude

$\theta$ - angle  = $75^o$

$\omega$ - angular displacement = $2\pi/T$ = 2.866 m

Put the values and calculate for $\omega$,

$75 = A\times{\rm \ cos}(2.866\times 2.191)\\\\75 =A \times cos\ 6.26\\\\A =\dfrac {75}{0.99}\\\\A = 75.75 \rm \ inches$

Therefore, the distance traveled by pendulum, in one back-and-forth swing is 75.75 inches.

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