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I'm having difficulty with this physics problem.

A small block that has a mass equal to $m_1$ rests on a piston that is vibrating vertically with simple harmonic motion described by the formula $y = A \sin(\omega t)$.

1)Show that the block will leave the piston if $\omega^2A > g$

2) If $\omega^2A = 3.01g$ and $A = 15.4$ cm, at what time will the block leave the piston?

I do not need to answer one, but I need help for two. My first thought was to plug into the equation and isolate $t$.

$A = 15.4 \text{ cm} = 0.154 \text{ m}$.

I'm not sure what y should be equal to. I'm also a little confused on the $\omega^2A = 3.01g$, because at first I thought it was a mass, but now I'm not sure.

Any help would be appreciated.

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  • $\begingroup$ Hint: the block leaves the piston when $\omega^2 A = g$. Find $\omega^2 A$ as a function of time and equate it to $g$ $\endgroup$
    – Aniruddha Deb
    May 2, 2020 at 3:11

1 Answer 1

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The block will leave the piston if the downward acceleration of the piston is greater than $g$. Your effort for $1$ was to find the condition where the acceleration at some point is greater than $g$. For $2$, what is $\omega$? You should differentiate the position of the piston twice with respect to time to get its acceleration, then find the time when it first becomes more negative than $-g$. Note that $15.4cm=0.154cm$ is false. I don't know what that line is doing here.

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