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A particle is oscillating about x=0 along x-axis. The potential energy is given by U=k|x| 3 where k is a positive constant. What is the time period of the oscillations of the particle?

A particle is oscillating about x=0 along x-axis. The potential energy is given by U=k|x|3 where  k is a positive constant. What is the time period of the oscillations of the particle?

Grade:12

1 Answers

pratham ashish
9 Points
12 years ago

Hi,

 

U asked about time period os the osccilation corresponding above Eqn 

 

but , hre this in not the case similiar to SHM , here time period depends on Amplitude

 

HOW?

if u compare the dimensions of both side then, the dimension of k = [ML-2T-2]

                                                  T  proportional to (mass)x(amplitude)y(k)z

                                                          RHS       = [M]x[L]y [ML-2T-2]z

                                                                     LHS =[T]

 

                                                              => x= 1/2 , y = z = -1/2

 

hence the time period depends over     1/sqrt(k)

 

this was good qn , we welcome all ur qns nd eager to asnweer them.

GOOD LUCK FOR UR PREPARATION

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