For a body to be in simple harmonic motion it shall satisfy some conditions.They are
1.The motion shall be oscillatory.
2.Acceleration of motion shall be directly proportional to displacement.
3.Acceleration shall be always directed to words its mean position.
If this three conditions are met then the oscillatory motion is said to be in simple harmonic motion.
Example :
Let us consider a particle vibrating back and forth about the origin of an x-axis between the limits +A and –A . In between these extreme positions the particle moves in such a manner that its speed is maximum when it is at the origin and zero when it is at ± A. The time t is chosen to be zero when the particle is at +A and it returns to +A at t = T.
Let us record its positions as a function of time by taking ‘snapshots’ at regular intervals of time.The position of the particle with reference to the origin gives its displacement at any instant of time. For such a motion the displacement x(t ) of the particle from a certain chosen origin is found to vary with time as,
x (t) = A cos ( ωt + φ) in which A, ω, and φ are constants.
The motion represented by equation is called simple harmonic motion (SHM); a term that means the periodic motion is a sinusoidal function of time. Equation in which the sinusoidal function is a cosine function.
The previous post is about What is periodic and Oscillatory Motion is ? Displacement in Oscillatory motion
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1.The motion shall be oscillatory.
2.Acceleration of motion shall be directly proportional to displacement.
3.Acceleration shall be always directed to words its mean position.
If this three conditions are met then the oscillatory motion is said to be in simple harmonic motion.
Example :
Let us consider a particle vibrating back and forth about the origin of an x-axis between the limits +A and –A . In between these extreme positions the particle moves in such a manner that its speed is maximum when it is at the origin and zero when it is at ± A. The time t is chosen to be zero when the particle is at +A and it returns to +A at t = T.
Let us record its positions as a function of time by taking ‘snapshots’ at regular intervals of time.The position of the particle with reference to the origin gives its displacement at any instant of time. For such a motion the displacement x(t ) of the particle from a certain chosen origin is found to vary with time as,
x (t) = A cos ( ωt + φ) in which A, ω, and φ are constants.
The motion represented by equation is called simple harmonic motion (SHM); a term that means the periodic motion is a sinusoidal function of time. Equation in which the sinusoidal function is a cosine function.
The previous post is about What is periodic and Oscillatory Motion is ? Displacement in Oscillatory motion
Time Period of Simple pendulum
Topics of Heat and ThermodynamicsHeat engine
Internal Energy
Zeroth law of thermodynamics
Thermodynamics Introduction
Heat transfer by radiation
Heat transfer by convection
Heat transfer and conduction
Heat and Temperature
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