A force $$F=$$−$$4x+8$$ (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 $$_______$$.

Question

A force $$F=$$−$$4x+8$$ (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 $$_______$$.

Infinity Learn · Accepted Answer

$$F=$$−$$4x+8=$$−$$4(x$$−$$2)=$$−$$4x0It$$ is equation of SHM.Mean position is x $$=$$ $$2$$ m, $$(as$$ F $$=$$ $$0)From$$ $$F=-4x0$$, K $$=$$ $$4N/mA=2EK1/2=(2)(32)41/2=4mThe$$ mean position is x $$=$$ $$2$$ mso, extreme positions of the points are $$6$$ m and $$-$$ $$2$$ m. The answer is $$6$$ m.

Simple harmonic motion

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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 _______.

$F = - 4 x + 8 = - 4 (x - 2) = - 4 x_{0}$
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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