What is the Amplitude in an SHM Problem?

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SUMMARY

The discussion focuses on determining the amplitude of a mass-spring system in simple harmonic motion (SHM). A 245 g mass oscillates at a frequency of 3.70 Hz, with initial conditions of position at 4.40 cm and velocity at -25.0 cm/s. The correct approach involves using both the position equation, \(x(t) = A \cos(\omega t + \phi)\), and the velocity equation, \(v(t) = -A \omega \sin(\omega t + \phi)\), to solve for the amplitude and phase constant. The user initially miscalculated the amplitude as 0.0440 m, which was incorrect.

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Finding amplitude? SHM problem

Homework Statement


A 245 g mass attached to a horizontal spring oscillates at a frequency of 3.70 Hz. At t =0s, the mass is at x= 4.40 cm and has v_x = -25.0 cm/s.
Determine:

Homework Equations


I got the first two
The Period= .27027 s
The Angular Frequency= 23.248 rad/s
The Amplitude=? m rounded to 5 sig figs
The Phase Constant=? rad rounded to 5 sig figs

The Attempt at a Solution



I tried using the equation (x)t=Acos(\omegat+\phi)
and plugged in t=0 and .0440m for x(0) so the answer i got was .0440m but this is wrong. and i can't attempt the phase constant yet because i need the Amplitude for that. Any help is appreciated thanks.
 
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jvick717 said:
I tried using the equation (x)t=Acos(\omegat+\phi)
and plugged in t=0 and .0440m for x(0) so the answer i got was .0440m but this is wrong. and i can't attempt the phase constant yet
Yes you can. You're off to the right start, but you'll need another equation to determine the phase constant. Hint: there's another value you're given in the problem that you haven't used. What can you do with it?
 


I'm guessing that the velocity has something to do with it and maybe the other equation for velocity v(t)= -A\omegasin(\omegat+\phi)??
 

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