A of mass 60 kg- standing on a platform- is executing SHM in a vertical plane- The displacement from mean position is y - 0-5 sin -2pi t- The minimum value of frequency -f- which the will feel weightlessness the highest point is - sqrt-g-2pi sqrt-2g-2pi sqrt-g-2pi- sqrt-3g-2pi

Question

A of mass 60 kg- standing on a platform- is executing SHM in a vertical plane- The displacement from mean position is y - 0-5 sin -2pi t- The minimum value of frequency -f- which the will feel weightlessness the highest point is - sqrt-g-2pi  sqrt-2g-2pi  sqrt-g-2pi-  sqrt-3g-2pi

Toppr Admin · Accepted Answer

W-2-x3C0-fA-0-5a-x2212-w2AFor weightlessness we have a-gThusg-x2212-w2Aw2-g0-5-2g4-x3C0-2f2-2gf2-g2-x3C0-2-f-x221A-2g2-x3C0-

A man of mass 60 kg, standing on a platform, is executing SHM in a vertical plane. The displacement from mean position is y=0.5sin(2πt). The minimum value of frequency (f) for which the man will feel weightlessness at the highest point is :√g/2π√2g/2π√g/2π√3g/2π

w=2πfA=0.5a=−w2AFor weightlessness we have a=gThusg=−w2Aw2=g0.5=2g4π2f2=2gf2=g2π2;f=√2g2π

$w = 2 π f$
$A = 0.5$
$a = - w^{2} A$
For weightlessness we have $a = g$
Thus
$g = - w^{2} A$
$w^{2} = \frac{g}{0.5} = 2 g$
$4 π^{2} f^{2} = 2 g$
$f^{2} = \frac{g}{2 π^{2}}; f = \frac{\sqrt{2 g}}{2 π}$