{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# shm - Simple Harmonic Motion THEORY Vibration is the motion...

This preview shows pages 1–2. Sign up to view the full content.

THEORY Vibration is the motion of an object back and forth over the same ground. The most important example of vibration is simple harmonic motion (SHM). One system that manifests SHM is a mass, m, attached to a spring where k is the spring constant. Let the system reside on a horizontal table with no friction present. If the mass is pulled back a distance x from the equilibrium it will experience a spring force that obeys Hooke’s law, F = - k x. Since this is the net force on m, by Newton’s second law, -k x = m d 2 x / dt 2 OR d 2 x / dt 2 + ϖ 2 x = 0 where ϖ 2 k/m, and ϖ is called the (angular) frequency of vibration = 2 π /T, T = period =1/f, and f is the frequency . Here is the first case where we are confronted with a non-constant acceleration. The above equation is called a differential equation because it contains both a function, x(t), as well as derivatives of the function. We will solve the differential equation two ways:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

shm - Simple Harmonic Motion THEORY Vibration is the motion...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online