Simple Harmonic Motion, BSc DOCX

Title	Simple Harmonic Motion, BSc
Author	Muhammad Azhar
Pages	4
File Size	70.5 KB
File Type	DOCX
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Summary

Lecture Notes Course 302 (Wave & Oscillation and Thermodynamics) By Muhammad Azhar PERIODIC MOTION: Any motion that repeats itself after regular intervals of time is known as a periodic motion. OSCILLATORY MOTION: The “to in fro” motion described by an object a whole, along the same path, withou...

Description

Lecture Notes Course 302 (Wave & Oscillatoo aod Thermodyoamics) By Muhammad Azhar PERIODIC MOTION: Any motion that repeats itself after regular intervals of time is known as a periodic motion. OSCILLATORY MOTION: The "to in fro" motion described by an object a whole, along the same path, without change in shape of object is called Oscillatory Motion. SIMPLE HARMONIC MOTION: It is the simple type of oscillatory motion in which acceleration of the vibrating object is directly proportional to the displacement. Examples: Motion of pendulum, Vibrating molecule, Motion of swing etc. CHARACTERISTICS OF SIMPLE HARMONIC MOTION: It is always periodic. Acceleration is directly proportional to the displacement but opposite in direction. Acceleration is always directed towards the mean position. It can be described by sine or cosine function. At mean position the K.E is maximum but P.E is zero. At extreme positions K.E is zero but P.E is Maximum. SPRING MASS SYSTEM: Consider a mass "m" is attached to a spring which placed on a smooth horizontal surface. If the system is slightly disturbed, it will start to in fro motion around the mean position. According to Hook's law F= kx ------> (1) According to Newton's second law F=ma ------> (2) Combining equation (1) and (2), we get ma= kx ----- (3) a= k m x Where k m = constant So, we can write a x The above equation shows that the motion of body attached with spring is Simple Harmonic Motion. Recall Eq. (3) ma= kx In derivative form m d 2 x dt2 = kx m d 2 x dt2 +kx=0 Wave Equation Departmeot of Physics, Uoiversity of Karachi...