Solving Spring Homework: Angular Frequency & Amplitude

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SUMMARY

The discussion focuses on solving a physics homework problem involving a block on a spring, specifically calculating the angular frequency and amplitude based on given positions and times. The equations used include the harmonic motion formula x(t) = A cos(wt + φ₀). The key insight is that by dividing the equations for the two positions at different times, the amplitude A cancels out, simplifying the process of solving for angular frequency w. This approach leads to a more manageable equation for w, facilitating the determination of both angular frequency and amplitude.

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Homework Statement


A block on a spring is pulled to the right and released at t=0s. It passes x=3.00cm at t=0.685s, and it passes x=-3.00cm at t=0.886s.
a) What is the angular frequency?
b) What is the amplitude?


Homework Equations


x(t)=Acos(wt+phi_0)


The Attempt at a Solution


Since the spring was initially pulled to the right, I assumed that the distance it was pulled would be the amplitude and with the initial conditions x0=Acos(phi_0)=A, I set phi_0=0. Plugging in the times and positions,
x(t=0.685s)=Acos(0.685w)
x(t=0.886s)=Acos(0.886w).
I tried solving for an equation for A and plugging it into the other equation, but it just ended up looking like a complicated mess. Any insight would be appreciated =)
 
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There might be some insight to be gained by observing that the times given are for equal but opposite displacements about 0. Presumably the block and spring are at rest at x = 0.
 
or you have

two equations
3.00=Acos(0.685w) and
-3.00=Acos(0.886w).

I would divide the equations, then A cancels, and you might have an easier time solving for w.
 

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