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A particle is...

Question

A particle is moving on x-axis has potential energy $U = 2 - 20 x + 5 x^{2}$ joules along x-axis. The particle is released at x = – 3. If the mass of the particle is 0.1 kg and the maximum velocity of the particle (in m/s) is 10x, the value of x is ___ .

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Solution

$F = 20 - 10 x = - 10 (x - 2)$

Comparing with the data, we get amplitude=5

Hence, force constant is k = 10 ; m = 0.1 kg

Angular frequency, $ω = \sqrt{\frac{k}{m}} = 10$ rad/s

$v_{m a x} = w A = 50 m / s$

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