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Starting from the origin,a body oscillates simple harmonically with a period of 2sec.After what time will it's kinetic energy be 75% of the total energy............... Pls explain......

Starting from the origin,a body oscillates simple harmonically with a period of 2sec.After what time will it's kinetic energy be 75% of the total energy...............


 


Pls explain......

Grade:12

1 Answers

Harish R
37 Points
11 years ago

Hey Vishwjit,

we can do this sum as follows:

TE of an SHM is given as 1/2m(wA)^2

K.E for any SHM can be written as 1/2 m(wA)^2 cos^2(wt). even if u dont know this dont worry, u can easily generalise this from the energy of spring-mass system.

so for 75% KE,

3/4 * 1/2 m(wA)^2=1/2 m(wA)^2 cos^2(wt)

=> ((3)^1/2)/2=cos(wt)

we get , wt = pi / 6

w=2 pi/T

t=T/12 = 1/6 seconds.

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