Question

A particle is moving on x-axis has potential energy $U=2-20x+5x^2$ 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 ___ .

Answer 1

$F=20-10x=–10(x-2)$

Comparing with the data, we get amplitude=5

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

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

$v_{max}=wA=50m/s$