# Simple harmonic motion of sliding dinner plate

• jimbo71
In summary, the child's dinner plate has a mass of 240 g and is being slid back and forth with SHM on a horizontal surface. The amplitude is 0.110 m and the speed at a distance of 7.00×10−2 m away from equilibrium is 0.350 m/s. The period and displacement when the speed is 0.160m/s can be calculated using the equations T=2pi(m/k)^1/2 and v^2 = \omega^2(a^2 - x^2). The angular frequency (omega) can be found by plugging in the given values, and the time period can be calculated using T = \frac{2\pi}{\omega}.
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.

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

For the second question, we can use the displacement equation to find the value of x when the speed is 0.160 m/s. For the third question, we can use the equation for the coefficient of static friction, mu_s = F_s/F_N, where F_s is the force of static friction and F_N is the normal force. We can find the normal force by using the weight of the carrot slice, mg, and the acceleration due to gravity, g. We can then use the equation for SHM to find the maximum force on the carrot slice, F_max = kA, where k is the force constant and A is the amplitude. Finally, we can use the equation for the coefficient of static friction to find the value of mu_s.

## 1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object moves back and forth in a straight line with a constant amplitude and a sinusoidal pattern. It is caused by a restoring force that is directly proportional to the displacement of the object from its equilibrium position.

## 2. How does the sliding dinner plate exhibit simple harmonic motion?

When a dinner plate is placed on a horizontal surface and given a small push, it will move back and forth in a straight line with a constant amplitude. This is because the plate is acted upon by the force of gravity and the normal force from the surface, which together act as restoring forces that cause the plate to oscillate.

## 3. What factors affect the period of simple harmonic motion in a sliding dinner plate?

The period of simple harmonic motion in a sliding dinner plate is affected by the mass of the plate, the magnitude of the restoring forces, and the angle at which the plate is displaced from its equilibrium position. The period is shorter for heavier plates, stronger restoring forces, and larger displacement angles.

## 4. Can the frequency of simple harmonic motion in a sliding dinner plate be changed?

Yes, the frequency of simple harmonic motion in a sliding dinner plate can be changed by altering the factors that affect its period, such as the mass of the plate, the magnitude of the restoring forces, and the angle of displacement. For example, a lighter plate or a stronger push will result in a higher frequency of oscillation.

## 5. What is the equation for calculating the period of simple harmonic motion in a sliding dinner plate?

The period of simple harmonic motion in a sliding dinner plate can be calculated using the equation T = 2π√(m/k), where T is the period in seconds, m is the mass of the plate in kilograms, and k is the spring constant of the restoring forces in Newtons per meter (N/m).

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