Simple Harmonic Motion Question

AI Thread Summary
A particle in simple harmonic motion (SHM) starts from rest and travels 1m in the first second and 2m in the second second. The maximum acceleration can be derived using the equations of motion for SHM, specifically relating displacement to amplitude and angular frequency. The discussion emphasizes using the distances traveled to set up equations that can be solved for the amplitude and angular frequency. Participants suggest substituting values into the SHM equations to find the necessary parameters. The thread concludes with a request for clarification on the approach to solving the equations effectively.
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Homework Statement


A particle moves with SHM in a straight line.
In the first second after starting from rest,it travels a distance of 1m in a constant direction.
In the next second, it travels a distance of 2m in the same direction.
Find its maximum acceleration


Homework Equations


x=acos(ωt)
\dot{x}=-ω√(a2-x2)
\ddot{x}=-ω2x


The Attempt at a Solution


Starting from rest ∴ when \dot{x}=0, x=a, \ddot{x}=maximum.
maximum \ddot{x}=-ω2x
maximum amplitude = 1.5
∴ amplitude \geq1.5

After many more lines of work, no solution was able to be found.
Can someone help?
 
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You have two equations and two unknowns, you don't need to do anything more than plugging values into x=acos(ωt).

From the given information what values do you suppose you need to plug in?
 
when t=1, x=a-1
when t=2, x=a-3
 
In the first second after starting from rest,it travels a distance of 1m in a constant direction.
In the next second, it travels a distance of 2m in the same direction.

I'd use this, what exactly is this saying?
 
it is saying that after the 1st second the particle has moved 1m from the amplitude position and that after the 2nd second the particle mas moved a total of 3m from the amplitude position.
 
You have
\begin{align*}
a - a \cos \omega &= 1 \\
a - a \cos 2\omega &= 3
\end{align*} Solve for a in the first equation and substitute into the other. Then use a trig identity for ##\cos 2\omega## to write it in terms of ##\cos \omega##.
 
ok. thank you for this. it helps me a lot
 
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