# Standard Harmonic Motion of a Plate

1. Dec 1, 2011

### vdipaola

A child with poor table manners is sliding his 240 dinner plate back and forth in SHM with an amplitude of 0.120 on a horizontal surface. At a point a distance 7.00×10−2 away from equilibrium, the speed of the plate is 0.370 .
(a) What is the period
(b)What is the displacement when the speed is 0.150 ?
(c)In the center of the dinner plate is a carrot slice of mass 10.9 . 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 .

I got 2.7 and .16 for the first two but neither are correct. Help please?

2. Dec 1, 2011

### Simon Bridge

1. How do you know they are not correct?
2. How did you attempt the problem?

The secret to these kinds of problems is to sketch the graph of position against time, and use that to approximate the velocity-time graph ... from there it will be obvious how the equations fit.

If you prefer - just work out what you know:

y(t)=Asin(ωt), v(t)=dy/dt (what is the equation of v(t)?)

y(T)=0.12 (what is A)

Asin(ωt')=0.07, v(t')=0.370
... gives you two equations with two unknowns.

3. Dec 1, 2011

### vdipaola

Okay I got it correct now, Thank You very much.

4. Dec 1, 2011

### Simon Bridge

Well done - and welcome to PF.