Oscillations

Any pendulum undergoes simple harmonic motion when the amplitude of oscillation is small. The pendulum still oscillates, but the motion is no longer simple harmonic motion because the angular acceleration is not proportional to the negative of the angular displacement.

amplitude

• Simple Harmonic Motion.
• Damped Simple Harmonic Motion.
• Forced Simple Harmonic Motion.
• Force Law for Simple Harmonic Motion.
• Velocity and Acceleration in Simple Harmonic Motion.
• Some Systems executing Simple Harmonic Motion.
• Energy in Simple Harmonic Motion.
• Periodic and Oscillatory Motion.

Does the acceleration of a simple harmonic oscillator remain constant during its motion? Is the acceleration ever zero? No. Acceleration is maximum when the restoring force is maximum (when the oscillator is changing direction) at the maximum displacement from equilibrium (EQ).

If the spring obeys Hooke’s law, then it always executes simple harmonic motion. It is clearly evident from the above equation that the acceleration is directly proportional to the displacement and acts in the direction opposite to the displacement.

A wave is a disturbance that transfers energy from one place to another without requiring any net flow of mass. There is a close connection between simple harmonic motion and periodic waves; in most periodic waves, the particles in the medium experience simple harmonic motion.

The period T and frequency f of a simple harmonic oscillator are given by T=2π√mk T = 2 π m k and f=12π√km f = 1 2 π k m , where m is the mass of the system. Displacement in simple harmonic motion as a function of time is given by x(t)=Xcos2πtT x ( t ) = X cos 2 π t T .

And, the simple harmonic motion is always oscillatory. Periodic motion examples are the motion of the hands of a clock, the motion of the wheels of a car, etc. Simple harmonic motion examples: the motion of a pendulum, motion of a spring, etc. Learn the difference between Periodic and Oscillatory Motion here.

All oscillatory motions are periodic motions but all periodic motions are not oscillatory. Simple harmonic motion is a straight line motion and it requires a restoring force.