Simple Harmonic Brain Buster...?

The position can be described as follows:

x = X.max * sin ( ( 2 π ƒ ) * t )

where X.max is the maximum displacement from the mean point "O"

Note, x = 0 and be over "O" when

sin ( ( 2 π ƒ ) * t ) = 0

The acceleration (and hence the force) can be described as follows:

a = d²x/dt²

a = - X.max * ( 2 π ƒ )² sin ( ( 2 π ƒ ) * t )

So, the acceleration is opposite the displacement and will always be directed towards O. This is because of the minus sign.

Moreover, the acceleration will have a maximum when

| sin ( ( 2 π ƒ ) * t ) | is at a maximum, i.e.,

| sin ( ( 2 π ƒ ) * t ) | = 1

This will occur when the coin is at its maximum displacement.

As for your last question

a = μ g

μ g = X.max * ( 2 π ƒ )² * 1

ƒ = 1/(2 π) √( μ g / X.max )

You will note that this is markedly similar to the equations for frequency for a spring and for a pendulum:

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I used "ƒ" as the frequency, not force

I used acceleration "a" rather than Force, i.e., m*a

The only force in the direction of travel will be the static frictional force. Without frictional force the coin would not move but the platform would.

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"O" is not on the platform. Imagine a glass platform that oscillates. My reading is that O would be underneath. Put a coin on the platform and you can watch it oscillate around point O. But it is the platform that is oscillating.

Since it is presumed that there is an external force on the platform and not on the coin, then the only thing holding the coin in place without slipping on the platform is friction. It will have the same acceleration as the platform. The only thing providing this acceleration is the frictional force. And yes, it will be directed to towards point O.

Not A because the inertia of rest of the coin is opposed when the platform starts from the extreme end hence the friction is in opposite direction to O.

B must be true. Take explaination for A. Also when the velocity of the coin drops when it crosses O the friction is towards O.

C is true because the friction is highest when the velocity drops after O. After that the friction constantly decreases with the velocity till it ultimately reaches 0 in the extreme end.

D is wrong as it contradicts C

I hope i am right this time. Well doesn't matter. Keep on posting such questions once in while atleast. :)

the frequency of oscillation is every morning whether I need it or not