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CBSE Class 11-science Answered

A particle of mass m moving in a field of conservative force with potential energy given by  u =  a  + bx^2  J/Kg is performing SHM. then the frequency of the shm can be
Asked by TheGreatScientist | 07 Mar, 2021, 01:19: PM
answered-by-expert Expert Answer
Potential energy U = a + b x2
 
Force due to potential  = -dU/dx = -2bx
 
Restoring force of SHM is in the form , F = - k x  , where k is force constant
 
Hence force constant k for given potential field , k = 2b
 
angular frequency ω of SHM is given as
 
begin mathsize 14px style omega space equals 2 pi f space equals space space square root of k over m end root space equals space square root of fraction numerator 2 b over denominator m end fraction end root end style
where f is frequency of SHM
 
begin mathsize 14px style f space equals fraction numerator 1 over denominator 2 pi end fraction space square root of fraction numerator 2 b over denominator m end fraction end root end style
Answered by Thiyagarajan K | 07 Mar, 2021, 02:04: PM
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