First slide

Simple harmonic motion

Question

A force $F = - 4 x + 8$ (inN) is acting on block where x is the position of block in metres. The energy of oscillation is 32 J. The block oscillates between two points, out of which value of position of one point (in m) is an integer from 0 to 9. The value of x is _______.

Moderate

Solution

$F = - 4 x + 8 = - 4 (x - 2) = - 4 x_{0}$
It is equation of SHM.
Mean position is x = 2 m, (as F = 0)
From F=-4x₀, K = 4N/m
$A = {[\frac{2 E}{K}]}^{1 / 2} = {[\frac{(2) (32)}{4}]}^{1 / 2} = 4 m$
The mean position is x = 2 m
so, extreme positions of the points are 6 m and - 2 m. The answer is 6 m.

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