derive the period of a simple pendulum and show that this is the period of a simple pendulum if whole mass is concentrated at thre center of the mass
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The motion is periodic, and we want to derive the expression for the period \( T \) of this pendulum. Show more…
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Show that the expression for the period of a physical penduhm reduces to that of a simple pendulum if the physical pendulum consists of a particle with mass $m$ on the end of a massless string of length $L .$
PHYSICS - PENDULUM A simple pendulum is formed by hanging a bob of mass $M$ on a string of length $L$ from a fixed support (see the figure). The time it takes the bob to swing from right to left and back again is called the period $T$ and is given by $$ T=2 \pi \sqrt{\frac{L}{g}} $$ where $g$ is the gravitational constant. Show that $T$ can be written in the form $$ T=\frac{2 \pi \sqrt{g L}}{g} $$
Basic Algebraic Operations
Exponents and Radicals
Consider the simple pendulum free body diagram, as shown in Figure 1b. When displaced by angle ̈θ, the component of the force of gravity on the mass, m, acts to pull the pendulum back toward vertical equilibrium, such that: Fnet = ma = -mgsinθ This second order differential equation has the familiar form describing simple harmonic motion. So, substituting in a solution of θ(t) = Asin(ωt + ϕ), we can show that: d²θ/dt² + (g/L)θ = 0 where L is the length of the pendulum and g is the acceleration due to gravity. This equation leads to a simple expression for the period, T. Before your lab session, provide a full derivation of ω and convert it to T, which you can use in your calculations.
Timothy J.
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