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?

i think -6

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

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

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.