Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

If the period of oscillation of a simple pendulum is 4s, find its length. If the velocity of the bob
at the mean position is 40cms−1
, find its amplitude. (take gravity = 9.81ms−2

Sagot :

deriyan191293

Answer:

Explanation:

Because we assume the pendulum is a "mathematical pendulum" (neglecting the moment of inertia of the bob), we can find:

[tex]T=2\pi\sqrt{\frac{L}{g}} \rightarrow 4=2\pi\sqrt{\frac{L}{9.81}} \rightarrow \frac{4}{\pi^{2}}=\frac{L}{9.81} \rightarrow L \approx 3.97 m[/tex]

By using the [tex]y=A\sin(\omega t) \rightarrow v = \frac{dy}{dt}=\omega A \cos\omega t = \omega\sqrt{A^{2}-y^{2}}[/tex]

The mean position is the position when y = 0, so:

[tex]\omega = \frac{2\pi}{T}=\frac{2\pi}{4}=0.5\pi[/tex] rad/s

and [tex]v = \omega A \rightarrow A=\frac{40}{0.5\pi}=\frac{80}{\pi}[/tex] in centimeters (cm).

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.