Simple harmonic motion equation

AI Thread Summary
The discussion revolves around determining the first time after t = 0 when the speed of an object in simple harmonic motion reaches its maximum. The relevant equation for simple harmonic motion is x = A sin(wt + φ), where A is the amplitude, and the initial position at t = 0 is given as 1.5 cm. The maximum displacement is noted as 3 cm, and the period is 2 seconds. To find the phase constant φ, the initial conditions are substituted into the equation, and then the velocity is derived from the position equation and set to zero to find the time. This approach provides a systematic method for solving the problem using the principles of 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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