Help with Simple Harmonic Motion

[cde42003]

I need help on a couple of problems.

1. A block on a spring is pulled to the right and released at t= 0s. It passes x = 3.0 cm at t= 0.685s, and it passes x= -3.0 cm at t= 0.886s.

What is the angular frequency?

What is the amplitude?

I know what equatios I need to use, but without knowing what the period is I can't figure out how to find the frequency. Once I have the period, I know how to figure the rest out so that is where I am stuck.

2. A penny rides on top of a piston as it undergoes vertical simple harmonic motion with an amplitude of 4.0 cm. If the frequency is low, the penny rides up and down without difficulty. If the frequency is steadily increased, there comes a point at which the penny leaves the surface.

What is the maximum frequency for which the penny just barely remains in place for the full cycle?

On this question, I honestly have no idea how to solve it. I know I need to relate the amplitude and the frequency together in some fashion, but do not know how or what to use to do this.

Thanks

 

[Pyrrhus]

1)

Analyze both data given in the equation $x = A \cos \omega t$

2)

When the normal force = 0, the penny is not in contact with the surface.

 

[cde42003]

Maybe I am missing something, but how can you use $x = A \cos \omega t$ when you do not know either A or omega?

 

[Pyrrhus]

Maybe I am missing something, but how can you use $x = A \cos \omega t$ when you do not know either A or omega?

You have x and t for 2 cases, so you can form a system of 2 equations.