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Simple Harmonic Motion

• Upon displacing an objects attached to one end of a spring, the other end being fixed, by a distance x, a restoring force equal to –kx, where k is the force constant of the spring, acts on the body.
• The force, being –kx, we can write Newton’s second law of motion as a differential equation. The solution of this differential equation gives oscillatory motion, or simple harmonic motion.
• The time to make one complete cycle is the period.
• In the spring-block system, the period of oscillation depends only on the mass of the block and the force constant of the spring.
• In the spring-block system, the total mechanical energy is the sum of the kinetic energy of the block and the elastic energy of the spring.
• The period of a pendulum depends only on the length of the pendulum and the value of g, the acceleration due to gravity.