A small block rests on a piston. When does the mass leave the piston?

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.

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

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.