Only parts d and e please. 1. In section 15.6, we derived an equation of motion for a simple pendulum where we assumed themass of the pendulum bob was a point mass particle with no physical size. We will now relax thatassumption. We will also consider the case where drag forces damp the motion of the pendulum.Ma.Consider a realistic pendulum as a uniform sphere of mass M and radius R at the end ofa massless string with length L being the distance from the pivot to the center of the sphere. Sketchthe physical situation. Label your diagram and list any knowns or unknowns for the problem.b.Find an expression for the period Treal of the real pendulum. Check your units and showthat if L >>R, your expression reduces to the period Tsimp for the simple point mass pendulumfound in section 15.6 of the text. By L >> R, we mean that L is much, much larger than R.C.Suppose L = 1.0 m, M = 25 g, R = 1.0 cm which are typical values for real pendulums.What is the numerical value of the ratio of Treal/Tsimp? Comment on the result by assessing of thevalidity of the point mass assumption.d.In our derivation of the equation of motion for the point mass pendulum, we alsoassumed there was no air resistance affecting the pendulum bob. We will now relax that assumptionby assuming a force due to air resistance to be proportional to the angular velocity with linear dragcoefficient b. This is a reasonable assumption since at low speeds air resistance is linear in velocity.The drag coefficient is a constant number that depends on the shape and frontal cross-sectional areaof the bob. Using techniques learned in class, derive an equation of motion for the simplependulum including air resistance. Use as the dependent variable and recall the small angleapproximation.e.Deduce the solutions 8(t) for the damped pendulum's equation of motion. Deduce anexpression for the period Tdamp of the damped pendulum. Show that if the drag coefficient b→ 0(and hence the drag force goes to zero), your expression reduces to the period Tsimp for the pointmass pendulum. (Hint: Look at section 15.7)

Name: Only parts d and e please. 1. In section 15.6, we derived an equation
Uploaded: 2024-03-20T06:58:04.000Z
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Description: Only parts d and e please. 1. In section 15.6, we derived an equation of motion for a simple pendulum where we assumed themass of the pendulum bob was a point mass particle with no physical size. We will now relax thatassumption. We will also conside