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Grade 12th PassMechanics

A particle moves under force F(x)=(x^2-6x)N,where x is in metres. For small displacements from the origin what is the force constant in the simple harmonic approximation?

Profile image of Raghav Dua
13 Years agoGrade 12th Pass
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4 Answers

Profile image of Vikas TU
ApprovedApproved Tutor Answer13 Years ago

i think -6

Profile image of Raghav Dua
13 Years ago

You are right the answer is 6 N/m but how can i solve it.Please Explain.

Profile image of AAYUSH KESHAVA
ApprovedApproved Tutor Answer13 Years ago

F(x)=x2-6x 

as x≈0 ,x2≈0 (as x2<<x)

so neglegting second degree term of x in expression, we get

F(x)=-6x 

on comparig with

F(x)=-kx 

we get k=6 units

Profile image of SOURAV MISHRA
12 Years ago

for small displacements x2 and other higher powers of x can be neglected in comparison to x.

so F(x) = -6x approximately.

therefore k = 6.

so the force constant in shm is 6 N/m.

please approve.