CBSE Class 11-science Answered
if the kinetic energy and potential energy becomes equal for a particle executing SHM, given by y=10sin5πt, then at that instance the displacement of the particle from the mean position is
Asked by binayakbiswas | 16 Mar, 2020, 09:25: AM
Expert Answer
Displacement y = 10 sin (5π t ) ................(1)
From eqn.(1), we get, angular frequency ω = 5π rad/s
if kinetic energy and potential energy are equal, then we have
(1/2) m v2 = (1/2) k y2 .....................(2)
where m is mass of particle , v is speed at time t and k = mω2 is force constant.
hence we get from eqn.(2), y = ± v/ω ................(3)
speed of particle is obtained by differentiating eqn.(1), v = 10 (5π) cos( 5πt ) ...............(4)
hence from eqn.(3) and (4), we get, y = ± 10 cos ( 5π t ) .....................(5)
Using eqn.(1), we write eqn.(5) as , 10 sin ( 5πt ) = ± 10 cos ( 5π t ) or tan (5πt) = ± 1 ............(6)
Hence we get , ( 5 π t ) = + π/4 or ( 5 π t ) = +3π/4
Hence time to get equal kinetic energy and potential energy is obtained as
t = 1/20 s or t = 3/20 s
Answered by Thiyagarajan K | 16 Mar, 2020, 03:24: PM
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