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The potential energy of a particle of mass 100 grams moving along x-axis is given by U=5x(x-4) where X is in metre the period of oscillation is

The potential energy of a particle of mass 100 grams moving along x-axis is given by U=5x(x-4) where X is in metre the period of oscillation is

Grade:12

1 Answers

Arun
25763 Points
3 years ago
Dear Vaibhav
I assume that U has been expressed in Joule.
The conservative force F = - dU/dx = 20 -10x = -10(x - 2) (Newton= N )
Let x-2 = X So, F = - 10 X = - k X where k = force constant or equivalent spring constant. Here k = 10 N /m. mass m =100 gram = 0.1 kg
Time period
T=2 π(m/k)^1/2 = 2 π(0.1/10)^1/2
= 2π/10
= π/5 second.
Oscillation shall occur about the point X= 0 => x-2 = 0 => x = 2
Regards
Arun (askIITians forum expert)

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