Simple harmonic motion of sliding dinner plate

[jimbo71]

Homework Statement

A child with poor table manners is sliding his 240 g dinner plate back and forth in SHM with an amplitude of 0.110 m on a horizontal surface. At a point a distance 7.00×10−2 m away from equilibrium, the speed of the plate is 0.350 m/s

1.What is the period?

2.What is the displacement when the speed is 0.160m/s?

3.In the center of the dinner plate is a carrot slice of mass 10.8 . If the carrot slice is just on the verge of slipping at the end point of the path, what is the coefficient of static friction between the carrot slice and the plate?
Take the free fall acceleration to be 9.80 .

Homework Equations

T=2pi(m/k)^1/2
x=Acos(omega*t+phi)
A=(x0^2+V0^2/omega^2)^1/2

The Attempt at a Solution

I don't know how to find the angular frequency or the force constant so I'm not sure how to find the period. Also I am confused about the amplitude in SHM equation because I'm not sure what X naught and V naught are.

 

[Galadirith]

Hi Jimbo, well first ill give you and equation that describes the velocity of a body in SHM that describes the velocity at a point at displacement x from its equilibrium position:

$$v^2 = \omega^2(a^2 - x^2)$$

where v is velocity, a our amplitude, x displacement and omega is our angular frequency (or angular velocity if wanting to go for a circular geometric interpretation).

so with this is should be evident that you can plug in some of the condition you were provided in the question to get omega.

Now from this I will also tell you of another equation

$$T = \frac{2\pi}{\omega}$$

so you can use omega to calculate the time period. I hope that helps with the first two questions of yours :D