# Motion of object (simple harmonic motion?)

• ~christina~
In summary, the conversation discusses the motion of a ball dropped from height 4.00m and its elastic collision with the ground. The questions revolve around showing that the motion is periodic, determining the period of motion, and whether the motion is simple harmonic. The suggested approaches include drawing a graph of position versus time, using conservation of mechanical energy, and looking to kinematic equations to find the time for one cycle.
~christina~
Gold Member

## Homework Statement

A ball dropped from height 4.00m makes an ellastic collision with the ground. Assuming no mechanical energy is lost to air resistance.

a) show that the motion is periodic

b) determine period of motion

c) is the motion simple harmonic?

## Homework Equations

not sure how to approach "showing motion is periodic" so I don't know what eqzn to use

## The Attempt at a Solution

a) show that the motion is periodic...

How would I technically show that??

I do know that it would be periodic since the ball hits the ground then bounces back up to the height it was dropped from but as to showing that...

b) period of motion.

well the period would be the time interval for the particle to go through one full cycle of motion but I'm not sure what to use there as well since in the book all they explain is the period as $$T= 2 \pi / \omega$$

can anyone help me out?

Thank you very much

Try to draw a graph of position versus time for the motion of the ball (it drops, and rises, with a constant acceleration/deceleration) and see how long it takes for the graph to repeat itself.

a) I'd suggest showing this with energy equations. conservation of mechanical energy will work.

b) You should look to your kinematic equations to find the time it takes to complete one cycle, down then back up again.

thanks

## 1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which the restoring force is directly proportional to the displacement of the object from its equilibrium position. This means that the object oscillates back and forth around its equilibrium point in a predictable pattern.

## 2. What are some examples of simple harmonic motion?

Some common examples of simple harmonic motion include a swinging pendulum, a mass attached to a spring, and the vibrations of a guitar string. These all exhibit the same pattern of back-and-forth motion around a central point.

## 3. How is simple harmonic motion different from other types of motion?

Simple harmonic motion is different from other types of motion because it follows a specific mathematical pattern known as a sinusoidal or sine wave. This pattern is characterized by a smooth, repetitive oscillation around a central point.

## 4. What factors affect the motion of an object in simple harmonic motion?

The motion of an object in simple harmonic motion is affected by three main factors: the mass of the object, the stiffness of the restoring force (such as the spring or pendulum), and the amplitude (or distance) of the motion. These factors determine the frequency and period of the oscillations.

## 5. How is simple harmonic motion used in real-world applications?

Simple harmonic motion has many practical applications in areas such as engineering, physics, and music. For example, it is used in the design of suspension systems in cars and buildings, in the creation of accurate clocks and timekeeping devices, and in the production of sound waves in musical instruments.

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