IIT JEE , AIEEE Forum - Physics , Mechanics

deep01

if <t> and denote the average kinetic energy and the average potential energies respectively of a mass executing a SHM, over one period, then the corresponding relation is

(A) <t>= -2 (B) <T>=+2

(C) <T>= (D) =2<t>

elessar_iitkgp

Let the instantaneous position of the particle be
x = A sin(

t +

)
v = A

cos(

t +

)

U = (1/2)m

²x² = (1/2)m

²A²sin²(

t+

)
 = (1/2)m

²A²<sin²(

t+

)> = (1/4)m

²A² (As <sin²(

t+

)> = 1/2)

T = (1/2)mv² = (1/2)m

²A²cos²(

t+

)
<T> = (1/2)m

²A²<cos²(

t+

)> = (1/4)m

²A² (As <cos²(

t+

)> = 1/2)

Hence = <T>

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