Simple harmonic motion and circular motion

In summary, uniform circular motion can be seen as a composition of two simple harmonic motions with the same frequency and a phase difference of pi/2. This is because the x and y coordinates of an object in uniform circular motion follow simple harmonic motion, with the x component being equivalent to the object's motion in the circle.
  • #1
gunparashar
7
0
why simple harmonic motion is projected as or compared with uniform circular motion ?
 
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  • #2
Because uniform circular motion is essentially "two dimensional simple harmonic motion."

Consider the shadow of an object moving in a circle when the light is shined "edge on". (This essentially "collapses" or "ignores" one of the dimensions of the motion)
 
  • #3
Well if one considers a cartesian coordinate system with origin at the center of the circle of the uniform circular motion, then can prove fairly easily that the x and y coordinates (of the particle that does circular motion), are doing simple harmonic motion. That is it will be x=R*cos(wt) and y=R*sin(wt) where w the angular velocity, R the radius of the circle.

So you can view uniform circular motion as composition of two simple harmonic motions of the same frequency, with phase differnce pi/2, and (thats important) of direction perpendicular to each other.
 
  • #4
The usual form the solution is given in, that is in terms of a shifted cosine, can be interpreted as the x component of a body in uniform circular motion.
 
  • #5


Simple harmonic motion and circular motion are both types of periodic motion, meaning they repeat in a regular pattern. However, they differ in their underlying principles and characteristics.

Simple harmonic motion is the motion of an object back and forth along a straight line, with a restoring force that is directly proportional to the displacement from the equilibrium position. This type of motion is often seen in systems such as a mass-spring system or a pendulum.

On the other hand, circular motion is the motion of an object along a circular path, with a constant speed. This type of motion is seen in systems such as a rotating wheel or a planet orbiting around a star.

Despite their differences, simple harmonic motion and circular motion can be compared and projected as similar in certain aspects. For instance, both types of motion exhibit a periodic nature, where the object repeats the same motion over and over again. Additionally, in both types of motion, the object experiences a restoring force that brings it back to its starting position.

Moreover, simple harmonic motion can be projected as or compared with uniform circular motion because the motion of an object in simple harmonic motion can be described as a projection of uniform circular motion along a straight line. This can be seen in the motion of a pendulum, where the circular motion of the pendulum bob is projected along the vertical axis.

Overall, simple harmonic motion and circular motion share some similarities and can be compared and projected as similar in certain aspects. However, it is important to note that they are distinct types of motion with their own unique characteristics and underlying principles.
 

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 single straight line, with its acceleration proportional to its displacement from a fixed point. Examples of simple harmonic motion include the swinging of a pendulum and the vibrations of a guitar string.

2. What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A sin(ωt + φ), where x is the displacement from the equilibrium position, A is the amplitude, ω is the angular frequency, and φ is the phase constant. This equation describes the position of the object at any given time during its oscillations.

3. What is circular motion?

Circular motion is a type of motion in which an object follows a circular path around a central point. This type of motion can be uniform, meaning the object moves at a constant speed, or non-uniform, meaning the object's speed and/or direction changes as it moves along the circular path.

4. What is the relationship between circular motion and simple harmonic motion?

There is a close relationship between circular motion and simple harmonic motion. Circular motion can be thought of as a projection of simple harmonic motion onto a circular path. This means that an object moving in a circular path with constant speed experiences simple harmonic motion in one direction, while an object moving in a straight line with simple harmonic motion experiences circular motion if viewed from a different perspective.

5. How are frequency and period related in simple harmonic motion?

The frequency and period of simple harmonic motion are inversely related. The frequency, measured in hertz (Hz), is the number of complete oscillations per second. The period, measured in seconds (s), is the time it takes for one complete oscillation. The relationship between frequency (f) and period (T) is given by f = 1/T.

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