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# Periodic Motion Assignment Help

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Classical Physics - Periodic Motion

**Periodic Motion**

If a moving body repeats its motion after regular intervals of time the motion is said to be harmonic or periodic. The time interval after which it repeats the motion is called time period. if the body moves to and fro on the same path, it is said to be oscillation. In simple harmonic motion the particle moves in a straight line and the acceleration of the particle is always infected towards a fixed point on the line. This fixed point is called centre of oscillation. The acceleration in **SHM** is given by

**a = - ω**^{2}x or F = - mω^{2}x = - Kx

**K = mω**^{2} is called the force constant or spring constant.

The force which brings the particle back towards the equilibrium (or mean) position is called restoring force.

**SHM **may be thought of as the projection of uniform circular motion along a diameter.

**X = r cos αx**

Y = r sin αx

Α = ω^{2} x

Or d^{2}x / dt^{2} = - ω^{2}x

Given the solution **x = x**_{0}sin αx

When the particle starts from mean position,

**X = x**_{0} cos ωt

When, starts from extreme position

**X = x**_{0} sin (ωt ± Ø**)**

X = x_{0} cos (ωt ± Ø**)**

When it starts in between mean and extreme positions.

**X = x**_{0} e ±iωt

Where** x** is called instantaneous displacement, **x**_{0} the amplitude (maximum displacement) Ø initial phase angle or epoch or angle of repose and **ω** the angular frequency.

**Linear frequency f = ω / 2π and T = 1 / ƒ is time period**

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**Periodic Motion**

**SHM**is given by

**a = - ω**

^{2}x or F = - mω^{2}x = - Kx**K = mω**

^{2}is called the force constant or spring constant.

The force which brings the particle back towards the equilibrium (or mean) position is called restoring force.

**SHM**may be thought of as the projection of uniform circular motion along a diameter.

**X = r cos αx**

Y = r sin αx

Α = ω

Or d

Y = r sin αx

Α = ω

^{2}xOr d

^{2}x / dt^{2}= - ω^{2}xGiven the solution

**x = x**

_{0}sin αxWhen the particle starts from mean position,

**X = x**

_{0}cos ωtWhen, starts from extreme position

**X = x**Ø

_{0}sin (ωt ±**)**

X = xØ

X = x

_{0}cos (ωt ±**)**

When it starts in between mean and extreme positions.

**X = x**

_{0}e ±iωtWhere

**x**is called instantaneous displacement,

**x**

_{0}the amplitude (maximum displacement) Ø initial phase angle or epoch or angle of repose and

**ω**the angular frequency.

**Linear frequency f = ω / 2π and T = 1 / ƒ is time period**

ExpertsMind.com - Physics Assignment Help, Periodic Motion Assignment Help, Periodic Motion Homework Help, Periodic Motion Assignment Tutors, Periodic Motion Solutions, Periodic Motion Answers, Classical Physics Assignment Tutors