Question

Question 3 40 pts A pendulum with length $L$ and mass $m$ is at an angle $\varphi$ from rest. Assuming the mass of the string is negligible, ignoring air resistance and assuming $\varphi \approx \sin \varphi$, derive the second order differential equation using Newton's second law in polar coordinates given by: $\frac{d^2\varphi}{dt^2} + \frac{g}{L}\sin\varphi = 0$. (you do not need to solve the differential equation).

          Question 3
40 pts
A pendulum with length $L$ and mass $m$ is at an angle $\varphi$ from rest. Assuming the mass of the string is negligible, ignoring air resistance and assuming $\varphi \approx \sin \varphi$, derive the second order differential equation using Newton's second law in polar coordinates given by: $\frac{d^2\varphi}{dt^2} + \frac{g}{L}\sin\varphi = 0$. (you do not need to solve the differential equation).

Question 3
40 pts
A pendulum with length L and mass m is at an angle φ from rest. Assuming the mass of the string is negligible, ignoring air resistance and assuming φ≈sinφ, derive the second order differential equation using Newton's second law in polar coordinates given by: (d^2φ)/(dt^2) + (g)/(L)sinφ = 0. (you do not need to solve the differential equation).

Added by Angela H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Frank Deng

Step 1

The only force acting on the pendulum bob is gravity, which can be resolved into two components: one along the direction of the string (tension) and one perpendicular to the string (restoring force). Show more…

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Question 3 40 pts A pendulum with length L and mass m is at an angle θ from rest. Assuming the mass of the string is negligible, ignoring air resistance and assuming sinθ, derive the second order differential equation using Newton's second law in polar coordinates given by: d²θ/dt² + sinθ = 0. (You do not need to solve the differential equation). Upload Choose a File