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Standard XII

Physics

Forced Oscillations

A particle mo...

Question

A particle moves under the force $F (x) = (x^{2} - 6 x) N$ , where x is in meters. Show that for small displacements from the origin the force constant in the simple harmonic motion is approximately 6.

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Solution

For small value of x, the term $x^{2}$ can be neglected.
$∴$ $F = - 6 x$
Comparing with $F = - k x$ , we get
$k = 6 N / m$

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A particle moves under the force F(x)=(x2−6x)N, where x is in meters. Show that for small displacements from the origin the force constant in the simple harmonic motion is approximately 6.

For small value of x, the term x2 can be neglected.∴ F=−6xComparing with F=−kx, we getk=6 N/m

A particle moves under the force $F (x) = (x^{2} - 6 x) N$ , where x is in meters. Show that for small displacements from the origin the force constant in the simple harmonic motion is approximately 6.

For small value of x, the term $x^{2}$ can be neglected.
$∴$ $F = - 6 x$
Comparing with $F = - k x$ , we get
$k = 6 N / m$