Simple Harmonic Motion - whats the displacement of the mass

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SUMMARY

The discussion centers on calculating the displacement of a mass undergoing Simple Harmonic Motion (SHM) with an initial velocity of 2 m/s and a natural frequency of 2 rad/s. The initial phase (φ) is determined to be π/2, as the mass starts at the equilibrium position. The displacement equation ψ = A cos(ωt + φ) is utilized to find the amplitude (A) and the displacement after 13.2 seconds. The problem is resolved by confirming the initial conditions and phase angle.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM)
  • Familiarity with the displacement equation ψ = A cos(ωt + φ)
  • Knowledge of angular frequency and its relation to natural frequency
  • Basic principles of energy conservation in SHM
NEXT STEPS
  • Calculate the amplitude (A) using the initial conditions provided
  • Explore the implications of phase angle (φ) in SHM
  • Learn about energy transformations in Simple Harmonic Motion
  • Investigate the effects of varying natural frequency on SHM behavior
USEFUL FOR

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

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Homework Statement


A mass on a spring obeys SHM.Given that the mass is initially at the equilibrium position,has an initial velocity of 2m/s,and a nastural frequency of 2 rad/s,Find A and φ
After 13.2 sec what's the displacement of the mass

Homework Equations


ψ=Αcos(ωt+φ)


The Attempt at a Solution


Is the initial velocity ,the maximum velocity ? Maybe yes. Is the initial phase (φ) zero ? I think so.
 
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the initial velocity IS the maximum velocity, at equilibrium, KE = max, PE = zero.

if you use your notation for the motion of the mass, ie the cosine term, then no, the phase is not zero, it has to be pi/2, because at T=0, psi must be zero because the mass is at equilibrium.
 
Thanks
Problem solved :)
 

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