Calculating Amplitude of Brick Separation from Piston with SHM

[nazarip]

A brick is resting atop a piston that is moving vertically with simple harmonic motion of period 1.08 s. At what amplitude will the brick separate from the piston?

I came across this question reviewing for my test next Thursday. Anyway, I can calculate the angular frequency using the period, but I am not sure what to do after that. Any help is appreciated.

 

[Tide]

What happens when the downward acceleration exceeds g? :-)

 

[nazarip]

I would say that the brick would fly off, but I would have guessed that the upward acceleration would have had to exceed g. Can you explain please?

 

[Tide]

I would say that the brick would fly off, but I would have guessed that the upward acceleration would have had to exceed g. Can you explain please?

That depends on how you start the oscillation! In either case, what happens if the acceleration exceeds g? Do you think the answer will be different in those two cases?

 

[nazarip]

So if the acceleration in the direction of the orcillation exceeds g the brick will fly off...? I tried taking the derivative of the velocity equation -wAsin(wt+phi) but I got a wrong answer. This question is driving me nuts...

 

[Tide]

I'm guessing there's a problem with your calculation. Why don't you show what you've done?

 

[nazarip]

ok here is what I did:

v=-wAsin(wt+phi)
a=dv/dt=-Aw^2cos(wt+phi)

I set phi=0 (maybe went wrong here?) and...wait a second, hmm. Ok, I had to set t=0 also, then I just solve for A. Nothing like solving a problem at 2:02 am. Thanks for the patience Tide.

 

[Duarh]

A funny thing to note is that in both cases (going up & down) what we're looking for is the _downwards_ acceleration to exceed g. The going upwards case is somewhat less intuitive at first than the going downwards one (were the piston disconnects because it's just 'running away' too fast), but it works like this: the brick will stay with the piston while the piston moves up to the equilibrium (since the piston will be constantly accelerating and 'pushing' the brick with it) and then it'll stay with the piston until the piston's acceleration reaches -g (until it's decelerating at a rate of g), when it'll be the brick running away from the piston, not the other way around.

(:D I'm as always bothered by the absence of the effects of air resistance and such in these problems)