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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?

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?

Grade:12th Pass

4 Answers

Vikas TU
14149 Points
8 years ago

i think -6

Raghav Dua
18 Points
8 years ago

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

AAYUSH KESHAVA
22 Points
8 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

SOURAV MISHRA
37 Points
8 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.

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