Simple Harmonic Motion is the motion of a pendulum that is swinging back and forth. It is also known as the oscillatory motion. Typically, it is the motion of a mass on a spring when it follows a linear elastic force that restores, based on Hooke’s Law. It flows with time and shows a resonant frequency. The equation,(Hookes Law) is “F= -kx”, F being Force, k being the constant, an x being the displacement.

Definitions: Amplitude ( A ): The biggest distance moved from equilibrium position. The object moves back and forth between the two positions of maximum displacement, at x = A and x = - A .

Period ( T ): The time to finish one cycle of motion. If it starts at t = 0 at x = A , then it gets back to x = A after one full period at t = T .

Frequency ( f ): The number of cycles completed.

When at the equilibrium position, the object is not stretched or compressed. If you were to put a pen on the swinging object, such as a swing, with a piece of paper moving across under it, you would notice the simple harmonic motion of the swing. When the swing is not moving, the mark on the page under it would go straight, because it is at it’s equilibrium position. But, if you pushed the swing, the sine curve will show. An example of a sine curve is :

The high points of the curve are known as crests, while the low points are troughs. The straight line is the midpoint. Also, “amplitude” means the distance from the midpoint to either the crest or trough. The top of a crest to the top of the next crest’s distance is known as the wavelength. The frequency is how frequently the vibration happens. The number of back and forth vibrations in a certain time is basically what the frequency is. The way in which we measure frequency is “hertz.” There are kilohertz (thousands of hertz, megahertz (millions of hertz) and gigahertz (billions of hertz).

Frequencies and Time

If you have the time of a vibrating object, then the frequency can be found. If you have the frequency of a vibrating object, then the time can be found. There are two equations you need to know.

Frequency= 1/Time Or Time= 1/Frequency

As an example, if a pendulum had made 4 vibrations in 1 second, then the frequency is 4 Hz. Therefore, the time needed for 1 vibration is ¼ second.