Pendulum - find maximum angular displacement

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SUMMARY

The maximum angular displacement of the pendulum described by the equation theta=0.2cos(8t) is definitively 0.2 radians, occurring when the cosine function reaches its maximum value of 1. At t=3 seconds, the rate of change of theta can be calculated using the derivative of the function, yielding a value of -1.6 radians per second. This analysis confirms that the problem can be solved using trigonometric properties and calculus without needing additional initial conditions.

PREREQUISITES
  • Understanding of trigonometric functions, specifically cosine.
  • Basic knowledge of calculus, including differentiation.
  • Familiarity with angular displacement concepts in physics.
  • Ability to graph functions for visual analysis.
NEXT STEPS
  • Study the properties of the cosine function and its maxima and minima.
  • Learn how to differentiate trigonometric functions to find rates of change.
  • Explore the application of calculus in physics, particularly in motion analysis.
  • Practice graphing trigonometric functions to visualize their behavior over time.
USEFUL FOR

Students studying physics or mathematics, particularly those focusing on pendulum motion and calculus applications in real-world scenarios.

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Homework Statement


A 15-centimeter pendulum moves according to the equation:

theta=0.2cos8t

where theta is the angular displacement from the vertical in radians and t is the time in seconds. Determine the maximum angular displacement and the rate of change of theta when t=3 seconds.


Homework Equations


See, here's where I get stuck. It doesn't seem like I'm given enough information to do ANYTHING with this problem. At first I thought I could find the absolute maximum value by solving for theta at the endpoints and critical numbers, but I don't have any endpoints. Any physics equations I could use go out the window as well, because I have no initial displacement or velocity or any such stuff.


The Attempt at a Solution


Insert an hour of frustrated grumbling here, with no results.
 
Physics news on Phys.org
Graph y=0.2cos8t to see the whole picture!
Or recall what value(s) of x make cos x a maximum. Graph y = cos x if you don't recall.
 

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