Respuesta :
The distance traveled by pendulum, in one back-and-forth swing is 75.75 inches.
The period of pendulum can be calculated by
[tex]T = 2\pi \sqrt {\dfrac Lg}[/tex]
Where,
[tex]T[/tex] - period
[tex]L[/tex] - length = 12 inches
[tex]g[/tex]- gravitational acceleration = [tex]\bold {9.8\rm \ m/s^2}[/tex]
Put the values,
[tex]T = 2\pi \sqrt {\dfrac {12}{9.8}}\\\\T = 2 \times 3.14 \times \sqrt {0.122}\\\\T = 2.191[/tex]
Now, the angular displacement of the pendulum can be calculated by,
[tex]\theta = A\times\rm \ cos(\omega T)[/tex]
Where,
[tex]A[/tex]- amplitude
[tex]\theta[/tex] - angle = [tex]75^o[/tex]
[tex]\omega[/tex] - angular displacement = [tex]2\pi/T[/tex] = 2.866 m
Put the values and calculate for [tex]\omega[/tex],
[tex]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[/tex]
Therefore, the distance traveled by pendulum, in one back-and-forth swing is 75.75 inches.
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