Question

Answer the question below. To earn full credit show all work/calculations/thinking. You may want to do this work by hand on paper and then share an image of that work rather than trying to type it all out.The time (T) it takes for a pendulum to make one full swing back and forth can be modeled by the equation T= 2 \pi \sqrt[]{ \frac{L}{g} } where the length of the pendulum is L and the acceleration due to gravity is g.If the acceleration due to gravity is 32 feet/second and the period equals 1 second, find the length to the nearest inch (12 inches = 1 foot).

Answer 1

Given the equation

$\text{ T=2 }\pi\sqrt[]{\frac{L}{g}}$

Given that g = 32 feet/sec and T = 1sec, we want to look for the value of L at this value

Substitute g=32 and T = 1 into the equation above

$\begin{gathered} \text{ T=2 }\pi\sqrt[]{\frac{L}{g}} \\ 1\text{=2 }\pi\sqrt[]{\frac{L}{32}} \\ \text{divide both sides by 2 }\pi \\ \frac{1}{\text{2 }\pi}=\sqrt[]{\frac{L}{32}} \end{gathered}$

square both sides

$\begin{gathered} (\frac{1}{\text{2 }\pi})^2=(\sqrt[]{\frac{L}{32}})^2 \\ \frac{1}{4\pi^2}=\frac{L}{32} \\ 4\pi^2L\text{ = 32} \\ L\text{ = }\frac{32}{4\pi^2} \\ L=0.81057\text{ foot} \end{gathered}$

But we are asked to leave the answer in inch, to achieve this, we will convert the 0.81057 feet to inch by multiplying by 12

L = 0.81057 x 12

L = 9.72684

L = 10 inch (to nearest inch)

The Length is 10 inches (to the nearest inch)