Simple harmonic motion equation

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SUMMARY

The discussion focuses on solving a problem related to simple harmonic motion (SHM) using the equation x = A sin(wt + φ). The key parameters identified include an amplitude (A) of 3 cm, an initial position (x) of 1.5 cm at t = 0 s, and a period of 2 s. To find the first time after t = 0 s when the speed reaches a maximum, the derivative of the position equation must be taken, set to zero, and solved for time (t). This approach leads to determining the phase constant (φ) and subsequently the maximum speed timing.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM) principles
  • Familiarity with trigonometric functions and their derivatives
  • Knowledge of the relationship between period, frequency, and angular frequency
  • Ability to manipulate and solve equations involving sine functions
NEXT STEPS
  • Learn how to derive the velocity equation from the position equation in SHM
  • Study the concept of phase constant (φ) in simple harmonic motion
  • Explore the relationship between maximum speed and amplitude in SHM
  • Investigate the effects of varying the period on the motion of SHM systems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and wave motion, as well as educators seeking to clarify concepts related to simple harmonic motion.

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Homework Statement



An object is undergoing simple harmonic motion. The graph shows the position of the object as a function of time. What is the first time after t = 0 s when the speed reaches a maximum?

http://www.learning.physics.dal.ca/dalphysicslib/Graphics/Gtype26/shm.47.jpeg

Homework Equations



I don't know what equation to use to figure this out. φ = φo + wt perhaps?

The Attempt at a Solution



Im told that position at t=0 gives phi_0. But still do not know how to use the equation nor figure out any of the variables. Help is needed!
 
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From the graph we get the following information. At t = 0 x = 1.5 cm, maximum displacent = 3cm, and period = 2s.
Wright the equation of simple harmonic motion x = Asin(wt + phi). In this put A = 3cm, t = 0 and x = 1.5 cm find phi. Next take derivative of the equation, which gives the velocity and put it equal to zero. And find t.
 
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