Calculating Distance in Simple Harmonic Motion with Period and Amplitude

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The discussion revolves around calculating the position of an object in simple harmonic motion given its period T_1 and amplitude A. The initial equation proposed was A*cos((2*pi/T_1)*t), but it was pointed out that this does not satisfy the initial condition of x = 0 at t = 0. The correct approach involves using the sine function, resulting in the equation x = A*sin(2*pi*t/T), which accurately reflects the object's position at time t without a phase shift. The clarification helped the original poster recognize their mistake and appreciate the prompt assistance from other participants. Understanding the correct trigonometric function is crucial for accurately modeling simple harmonic motion.
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the question is
An object is undergoing simple harmonic motion with period T_1 and amplitude A. At t = 0 the object is at x = 0. How far is the object from the equilibrium position at time t?

well i come up with:
A*cos((2*pi/T_1)*t)

but i get that there's something wrong with my trigonometry, i can't figure out what I am doing wrong
 
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enclosed said:
the question is
An object is undergoing simple harmonic motion with period T_1 and amplitude A. At t = 0 the object is at x = 0. How far is the object from the equilibrium position at time t?
well i come up with:
A*cos((2*pi/T_1)*t)
but i get that there's something wrong with my trigonometry, i can't figure out what I am doing wrong

Hint: if you substitute t=0, do you get x=0 with that cosine function?

Zz.
 
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Well as the object is at the equilibrium position at t = 0 there's no phase shift and the displacement is modeled as x = Asin(wt)

The period (let's just call it T for now) = 2pi/w, therefore w = 2pi/T

The equation for the displacement at time t then comes to x = Asin(2*pi*t/T), so unless I'm mistaken you just misread the initial conditions (if you wanted to make it into a cos expression you could give it a phase shift of pi/2).

Cheers,
Just some guy
 
OMG thanks so much, i noticed the mistake, hehe, its pretty late, should be sleeping not prepping for my upcoming middies..
Thanks guys for quick replies!
 
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