Simple Harmonic Motion Assignment Help

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Any motion which replaces it after regular interval of time is called periodic or harmonic motion.

When the body of a pendulum moves to and fro through a short angle, the bob is called move simple harmonically. Current can be considered simple harmonic due to simple harmonic vibrations of electric and magnetic forces. In part of periodic motion, force is always directed towards a fixed point which may or may not be on the way of motion. Simple harmonic motion is closely associated with circular rotation. An example is shown below. This explains an arrangement used to convert circular motion of a stone D into the to and fro or simple harmonic motion of a point P.

1724_Simple Harmonic Motion.png

If a particle in periodic motion moves back and forth (or to and fro) over the similar path, then its motion is known as vibratory or oscillatory. The examples of vibratory or oscillatory motion are:

1. The motion of a pendulum.

2. The motion of a spring fixed at one side, which is compressed or stretched and then released.

3. The motion of a violin string.

4. The motion of atoms in molecules or in a solid lattice.

5. The motion of air molecules as sound wave passes by.

Important points regarding SHM:

1. Particle moves in straight line and the motion is periodic

2. The acceleration of particle is always proportional to the displacement from the equilibrium position and always directed towards a fixed point.

3. The work of the force is to bring particle in its equilibrium position and generally it is called restoring force.

4. In case of simple harmonic motion, the time period is independent of amplitude.

5. The necessary and sufficient condition for a motion to be simple harmonic is that the restoring force must be linear.

6. Every motion can be resolved into a number of simple harmonic motion with the help of Fourier analysis .i.e. any number of simple harmonic motion can be combined to give the resultant motion.

Conditions of Simple Harmonic Motion

            For SHM to occur, three conditions must be satisfied.

1. There must be a position of stable equilibrium.

            At the equation in equilibrium potential energy is minimized.

            That is, 911_Simple Harmonic Motion1.png    

2. There must be no dissipation of energy.

3. The acceleration is proportional to the displacement and opposite in direction.

            That is 19_Simple Harmonic Motion2.png,                                                           

SHM and g: If a small coin is placed on a horizontal platform connected to a vibrator and the amplitude is kept constant as the frequency is increased from zero,  the face will be heard chattering at a particular frequency fo. At this stage the reaction of the platform with the coin becomes zero at some part of every turn, so that it replaces contact periodically with the surface.

The maximum acceleration in SHM occurs at the end of the oscillation because the acceleration is directly proportional to the displacement. This maximum acceleration is w2r, where r is the amplitude and w is 2∏fo.

The coin will lose contact with the surface when it is moving down with acceleration g.  

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