# Question Solved1 AnswerAs you will learin in Chapter 3 ( , the angular acceleration of a simple pendulum is given by $$\ddot{\theta}=-(g / L)$$ sin $$\theta$$, where $$g$$ is the acceleration of gravity and $$I$$ is the length of the pendulum cord. Problem $$2.72$$ Derive the expression of the angular velocity $$\theta$$ as a function of the angular coordinale $$As you will learin in Chapter 3 ( , the angular acceleration of a simple pendulum is given by \( \ddot{\theta}=-(g / L)$$ sin $$\theta$$, where $$g$$ is the acceleration of gravity and $$I$$ is the length of the pendulum cord. Problem $$2.72$$ Derive the expression of the angular velocity $$\theta$$ as a function of the angular coordinale $$\theta$$. The initial conditions are $$(0)=\omega_{0}$$ and $$\theta(0)=\theta_{0 .}$$ Problem 2.73i Let the length of the pendulum cord be $$1=1.5 \mathrm{~m}$$. If $$\theta=3.7 \mathrm{rad} / \mathrm{s}$$ when $$\theta=14^{\circ}$$, determine the maximum value of $$\theta$$ achieved by the pendulum. The given angular acceleration remains valid even if the pendulum cord is replaced by a massless rigid bar. For this case, let $$L=$$ $$5.3 \mathrm{ft}$$ and assume that the pendulum is placed in motion at $$\theta=0^{\circ}$$. What is the minimum angular velocity at this position for the pendulum to swing through a full circle?

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Transcribed Image Text: As you will learin in Chapter 3 ( , the angular acceleration of a simple pendulum is given by $$\ddot{\theta}=-(g / L)$$ sin $$\theta$$, where $$g$$ is the acceleration of gravity and $$I$$ is the length of the pendulum cord. Problem $$2.72$$ Derive the expression of the angular velocity $$\theta$$ as a function of the angular coordinale $$\theta$$. The initial conditions are $$(0)=\omega_{0}$$ and $$\theta(0)=\theta_{0 .}$$ Problem 2.73i Let the length of the pendulum cord be $$1=1.5 \mathrm{~m}$$. If $$\theta=3.7 \mathrm{rad} / \mathrm{s}$$ when $$\theta=14^{\circ}$$, determine the maximum value of $$\theta$$ achieved by the pendulum. The given angular acceleration remains valid even if the pendulum cord is replaced by a massless rigid bar. For this case, let $$L=$$ $$5.3 \mathrm{ft}$$ and assume that the pendulum is placed in motion at $$\theta=0^{\circ}$$. What is the minimum angular velocity at this position for the pendulum to swing through a full circle?
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Transcribed Image Text: As you will learin in Chapter 3 ( , the angular acceleration of a simple pendulum is given by $$\ddot{\theta}=-(g / L)$$ sin $$\theta$$, where $$g$$ is the acceleration of gravity and $$I$$ is the length of the pendulum cord. Problem $$2.72$$ Derive the expression of the angular velocity $$\theta$$ as a function of the angular coordinale $$\theta$$. The initial conditions are $$(0)=\omega_{0}$$ and $$\theta(0)=\theta_{0 .}$$ Problem 2.73i Let the length of the pendulum cord be $$1=1.5 \mathrm{~m}$$. If $$\theta=3.7 \mathrm{rad} / \mathrm{s}$$ when $$\theta=14^{\circ}$$, determine the maximum value of $$\theta$$ achieved by the pendulum. The given angular acceleration remains valid even if the pendulum cord is replaced by a massless rigid bar. For this case, let $$L=$$ $$5.3 \mathrm{ft}$$ and assume that the pendulum is placed in motion at $$\theta=0^{\circ}$$. What is the minimum angular velocity at this position for the pendulum to swing through a full circle?