Simple Harmonic Motion Pendulum problem

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Homework Help Overview

The problem involves a simple pendulum of length 30.0 cm released from an angle of 10.0 degrees to the vertical, with the goal of finding its maximum speed under the assumption of simple harmonic motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between amplitude and the vertical height of the pendulum, questioning the calculation of amplitude and its implications for maximum speed.

Discussion Status

Some participants are clarifying the definition of amplitude in the context of the problem and exploring how it relates to the pendulum's position at a given angle. There is an ongoing examination of the calculations presented, with no clear consensus reached yet.

Contextual Notes

There is a potential misunderstanding regarding the definition of amplitude and its calculation from the pendulum's height at a specific angle. Participants are also considering the implications of the pendulum's motion and the equations involved.

bobbricks
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Homework Statement


A simple pendulum of length =30.0cm is released from rest from an angle of θ=10.0∘ to the vertical.
Assuming that the pendulum undergoes simple harmonic motion, find its maximum speed.

Source: https://isaacphysics.org/questions/accuracy_shm_pendulum_num

Homework Equations


a) v=wA
b) T=2pi*root(L/g) --possibly?

The Attempt at a Solution


A=0.3-0.3cos10
w=2pi/T
so w=root(g/L) by subbing equation a) into b).
g=9.81 and L=0.3.

so v=root(9.81/0.3)*(0.3-0.3cos10)
=0.02606... ms^(-1)

But that isn't the correct answer?
 
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A is the amplitude of oscillation, not the length of the pendulum.
 
Is A=0.3-0.3cos10 ?
 
Bump
 
bobbricks said:
Is A=0.3-0.3cos10 ?

How did you come up with this number? How far away from the equilibrium is the pendulum when it is at an angle of 10 degrees?
 
Its maximum velocity will be at the lowest point. The total length is 0.3m. Its current vertical height distance from the top is 0.3cos10. So the difference is 0.3-0.3cos10 which is the maximum amplitude..?
 

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