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.

• Displacement of particle executing SHM: $$x = A \cos(\omega t + \phi).$$

• Velocity of particle executing SHM: $$v = -A\omega \sin(\omega t + \phi).$$

• Acceleration of particle executing SHM: $$a = -A\omega^2\cos(\omega t + \phi).$$

• Time period of SHM: $$T = 2\pi/\omega.$$

• Frequency of SHM: $$f=\omega/2\pi.$$

• Amplitude of SHM: Maximum displacement from the mean position.

• Phase angle of SHM: Angle between the initial position of particle and the positive direction of the displacement axis at time t= 0.

• Energy of a particle executing SHM: $$E = \frac{1}{2}kA^2$$

• Potential energy of a particle executing SHM: $$U=\frac{1}{2}kx^2.$$

• Kinetic energy of a particle executing SHM: $$K = E-U = \frac{1}{2}kA^2(1-\cos^2\omega t).$$