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A person of mass 60 kg stands on a platform executing SHM in the vertical plane . The displacement from the mean position varies as y = 0.5 sin ( 2π f t ) . The value of f for which the person will feel weightlessness at the highest point is ( y is in metres ) –

Varun , 8 Years ago
Grade 12
anser 2 Answers
Vikas TU

Last Activity: 8 Years ago

From the condition, we can discover that 
    Angular speed = 2π f 
    y = 0.5 sin(2π f t) 
    dy/dt = 0.5 cos(2π ft) 2π f 
    Angular vel. = 0.5cos(2π ft) 2π f 
    2π f = 0.5 cos(2π ft) 2π f 
    1 = 0.5 cos(2π ft) 
    2 = cos(2π f) 
    Cos-1(2) =2π f 
   f= Cos-1(2)/2π 

Aakriti

Last Activity: 6 Years ago

For man to feel weightlessness, at highest point, acc= g
W^2A= g
where (w= 2πf and A= 0.5) 
puttingthe values in eq- we get the value of 'f'

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