14.22 Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals the average potential energy over the same period.

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Vishal Baghel | Contributor-Level 10

8 months ago

The equation of displacement of a particle executing SHM at an instant t is given bas:

x = Asin $ω t$ , where A = Amplitude of oscillation and $ω$ = angular frequency = $\sqrt{\frac{k}{M}}$

The velocity of the particle, v = $\frac{d x}{d t}$ = A $ω \cos ? ω t$

The kinetic energy of the particle $E_{k}$ = $\frac{1}{2}$ M $v^{2}$ = $\frac{1}{2}$ M ${(A ω \cos ? ω t)}^{2}$ = $\frac{1}{2}$ M $A^{2} ω^{2} {c o s}^{2} ω t$

The potential energy of the particle $E_{p}$ = $\frac{1}{2}$ k $x^{2}$ = $\frac{1}{2}$ k

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physics ncert solutions class 11th 2023

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