Question

a pendulum is l meters long. the time, t, in seconds that it takes to swing back and forth once. what is its length? the time, t, in seconds that it takes to swing back and forth once is given by t = 2√l. suppose the pendulum takes 7.86 seconds. carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth.

Explanation:

Step1: Given the formula for time of pendulum swing

$t = 2\sqrt{L}$

Step2: Substitute the given time value

We know $t=7.86$, so $7.86 = 2\sqrt{L}$

Step3: Solve for $\sqrt{L}$

$\sqrt{L}=\frac{7.86}{2}=3.93$

Step4: Solve for $L$

$L=(3.93)^2 = 15.4449$

Step5: Round to the nearest tenth

$L\approx15.4$

Answer:

$15.4$