Physics

$E=K+U$

$K_{avg}=U_{avg}=2E =41 mω_{2}A_{2}$

Note:

Average kinetic energy can also be found using $K_{avg}=T1 ∫_{0}Kdt$

Average potential energy can also be found using $U_{avg}=T1 ∫_{0}Udt$

It is often useful to find the equation of SHM.

Example:

A particle of mass $10$ gm is placed in a potential field given by $V=(50x_{2}+100)J/kg$. Find the frequency of oscillation in cycle/sec.

Solution:

Potential energy $U=mV$

$⇒U=(50x_{2}+100)10_{−2}$

$F=−dxdU =−(100x)10_{−2}$

$⇒mω_{2}x=−(100×10_{−2})x$

$10×10_{−3}ω_{2}x=100×10_{−2}x$

$⇒ω_{2}=100,ω=10$

$⇒f=2πω =2π10 =π5 $

It is often useful in finding equation of SHM and helps in solving problems.

$w=cpv $

p is the sound pressure.

v is the particle velocity in the direction of propagation.

c is the speed of sound.

$K.E.=∫2ρv_{2} dV$

Example.

$P.E.=41 μω_{2}A_{2}λ$

where,

$μ=$ Linear mass density,

$ω=$ Angular frequency,

$A=$ Amplitude of wave.

The velocity of a sound wave in $v$ and the wave energy density is $E,$ then find the amount of energy transferred per unit area per second by the wave in a direction normal to the wave propagation.

Solution:

Energy transferred in normal direction to the wave propogation is also known as intensity

$I=21 ρa_{2}ω_{2}v$

$E=ω_{2}a_{2}ρ$

hence $I=Ev$

ExampleDefinitionsFormulaes

ExampleDefinitionsFormulaes