Simple Harmonic Motion for a block-spring system

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SUMMARY

The discussion centers on calculating the ratio of kinetic energy (KE) to potential energy (PE) for a block-spring system undergoing simple harmonic motion (SHM) with a phase angle of π/5 radians. The equations used are PE = (1/2)*k*(xm^2)*cos^2(ωt + φ) and KE = (1/2)*k*(xm^2)*sin^2(ωt + φ). The user initially calculated KE/PE as sin²(φ)/cos²(φ) but encountered an error due to their calculator being set to degrees instead of radians. Correcting the calculator settings resolved the issue.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Familiarity with kinetic and potential energy equations in physics
  • Ability to work with trigonometric functions and phase angles
  • Knowledge of calculator settings for radians and degrees
NEXT STEPS
  • Review the principles of simple harmonic motion and its equations
  • Study the relationship between kinetic and potential energy in oscillatory systems
  • Learn how to convert between radians and degrees in calculations
  • Explore advanced applications of SHM in real-world systems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for examples of SHM applications.

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Homework Statement



If the phase angle for a block-spring system in SHM is π/5 rad and the block's position is given x = xm cos(ωt + phi), what is the ratio of the kinetic energy to the potential energy at time t = 0?

Homework Equations



PE = (1/2)*k*[(max amplitude)^2]*cos^2(ωt + phi)
KE = (1/2)*k*[(max amplitude)^2]*sin^2(ωt + phi)

Solve for KE/PE in that form.

The Attempt at a Solution



I took KE and divided by PE, giving sin^2(phi)/cos^2(phi). Plugging in pi/5 for phi gives us 1.20253316E-4/.99987974669. However, the system is saying this is wrong . I do believe that I solved for KE/PE correctly. Any help would be much appreciated. Thanks very much!
 
Physics news on Phys.org
Have you set your calculator to RAD? pi/5 is in radians.

ehild
 
I knew I was doing it right! my calculator was in degrees...i hate it when that happens...thanks for helping me figure that out!
 

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