Calculating Amplitude of a Simple Pendulum

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SUMMARY

The discussion focuses on calculating the amplitude of a simple pendulum with a mass of 0.052 kg and a thread length of 920 mm, released from a 5-degree angle. The amplitude is determined using the formula for vertical height, which involves the sine function. The correct calculation yields an amplitude of approximately 80 mm when rounded to two significant figures. Clarifications regarding the measurement points and definitions of amplitude are essential for accurate calculations.

PREREQUISITES
  • Understanding of basic trigonometry, specifically sine and tangent functions.
  • Familiarity with the physics of pendulums and oscillatory motion.
  • Knowledge of significant figures and their importance in scientific calculations.
  • Ability to interpret and manipulate equations related to pendulum motion.
NEXT STEPS
  • Study the derivation of pendulum motion equations, focusing on amplitude calculations.
  • Learn about the effects of angle on pendulum amplitude and period.
  • Explore the relationship between pendulum length and oscillation frequency.
  • Investigate the impact of mass and shape on pendulum dynamics.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify pendulum concepts in their curriculum.

Mattmiles
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Homework Statement



A simple pendulum consists of a spherical bob of mass 0.052 kg and diameter 1.1 cm attached to a thread of length 920 mm.

b) The bob is released at rest with the thread taut at an angle of 5 degrees to the vertical. Calculate:
i) the amplitude of the oscillation


Homework Equations





The Attempt at a Solution



Am I right in saying it is tan(5) * 920 = 80mm round to 2 sig fig?
 
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First we would need more information. I assume the string is attached at the top of the ball. Is that correct? So the total length of the pendulum is 93.1 cm? Where, on the pendulum are you measing to? The top, center, or bottom of the ball? And, what exactly do you mean by "amplitude"- the height the pendulum rises, the horizontal distance it covers, or the length of the arc? The last is the one I would assume but that is just the length of the pendulum times the angle in radians. And none is length times sin(5 degrees). That is the distance from the pivot point down to the height of the top of the pendulum at its highest point. The height it rises, the first of the three choices I mention, would be the length of the pendulum minus that.
 

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