# Simple Harmonic Motion and Reference Circle

• Pius
In summary, the conversation is about a 3.0-kg block between two horizontal springs. The block is initially at position x=0m and is then displaced 0.070m and released from rest. The questions asked are: (a) What is the speed of the block when it passes back through x=0m? (b) What is the angular frequency of the system? The formula for angular frequency is mentioned, but the individual is unsure of how to use it and is seeking help.
Pius

## Homework Statement

A 3.0-kg block is between two horizontal springs. Neither spring is trained when the block is at the position labeled x=0 m in the drawing. The block is then displaced a distance of 0.070m from the position where x=0m and is released from rest. (a) What is the speed of the block when it passes back through the x=0 position? (b) Determine the angular frequency w of this system.

I have no idea.

## The Attempt at a Solution

Help me!

Last edited:
How does angular frequency relate to the frequency of cycles?

omega!=2pi/T
7.54*10^4= 2pi*f
f=12006
12006*2.5s= 30016 times?
It says to use three significant digits from start to finish. How do I do that? Sorry, I haven't learned this!
Thanks danago!

## 1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object moves back and forth along a straight line, with the restoring force proportional to the displacement from the equilibrium position. This motion is characterized by a sinusoidal curve and is seen in many natural and man-made systems, such as a pendulum or a spring.

## 2. How does simple harmonic motion relate to the reference circle?

The reference circle is a tool used to visualize the motion of an object undergoing simple harmonic motion. The radius of the circle represents the maximum displacement of the object, and the angle of rotation of the circle corresponds to the position of the object along its path. The projection of the object's motion onto the reference circle creates a sinusoidal curve.

## 3. What factors affect the period of simple harmonic motion?

The period of simple harmonic motion is affected by two factors: the mass of the object and the spring constant of the system. A larger mass will result in a longer period, while a larger spring constant will result in a shorter period. The period of the motion is also independent of the amplitude or maximum displacement of the object.

## 4. Can simple harmonic motion occur in more than one dimension?

Yes, simple harmonic motion can occur in more than one dimension. In one dimension, the object moves back and forth along a straight line. In two dimensions, the object moves in a circular or elliptical path, but still follows the characteristics of simple harmonic motion, such as a sinusoidal curve.

## 5. What is the relationship between simple harmonic motion and energy?

Simple harmonic motion is a conservative system, meaning that energy is conserved. The kinetic energy of the object is at its maximum when it passes through the equilibrium position, and the potential energy is at its maximum when the object is at its maximum displacement. The total energy of the system, the sum of kinetic and potential energy, remains constant throughout the motion.

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