kinetic energy is x thn time period is proportional to
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Kinetic energy = (½)(m)(v^2)
So, x = ½mv^2 ...(1)
We know that, velocity = distance/time
which means, v = s/t
Substituting the value of v in equation (1),
x = ½m(s/t)^2
x = ½m(s^2/t^2)
Now,
t^2 = (½ms^2)/x = (ms^2)/2x
Taking square roots on both sides,
t = √[(ms^2)/2x]
t = s√(m/2x)
So, Time period = s√(m/2x)
So, x = ½mv^2 ...(1)
We know that, velocity = distance/time
which means, v = s/t
Substituting the value of v in equation (1),
x = ½m(s/t)^2
x = ½m(s^2/t^2)
Now,
t^2 = (½ms^2)/x = (ms^2)/2x
Taking square roots on both sides,
t = √[(ms^2)/2x]
t = s√(m/2x)
So, Time period = s√(m/2x)
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