Introduction To Simple Harmonic Motion
Concepts to remember on Introduction to Simple Harmonic Motion for JEE and CBSE board exams:
- SHM: Periodic motion where restoring force is ∝ -ve displacement from mean position.
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Displacement of particle executing SHM: $$x = A \cos(\omega t + \phi).$$
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Velocity of particle executing SHM: $$v = -A\omega \sin(\omega t + \phi).$$
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Acceleration of particle executing SHM: $$a = -A\omega^2\cos(\omega t + \phi).$$
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Time period of SHM: $$T = 2\pi/\omega.$$
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Frequency of SHM: $$f=\omega/2\pi.$$
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Amplitude of SHM: Maximum displacement from the mean position.
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Phase angle of SHM: Angle between the initial position of particle and the positive direction of the displacement axis at time t= 0.
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Energy of a particle executing SHM: $$E = \frac{1}{2}kA^2$$
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Potential energy of a particle executing SHM: $$U=\frac{1}{2}kx^2.$$
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Kinetic energy of a particle executing SHM: $$K = E-U = \frac{1}{2}kA^2(1-\cos^2\omega t).$$
