Question

If the potential energy of the particle is given by: U = x^2-8x+16. It starts from rest from x=0. What will be its maximum speed during SHM? Assume the mass of the particle to be 1kg.

(a) 4√2m/s

(b) 8m/s

(c) 2√2m/s

(d) 2√6m/s

The question was asked during a job interview.

The question is from Oscillations in division Oscillations of Physics – Class 11

Answer 1

Correct choice is (a) 4√2m/s

The explanation is: F = -dU/dx = 8 – 2x.

Particle starts from x=0, so force will increase its speed till force becomes zero at x=4.

Let acceleration be ‘a’.

a = dv/dt = v dv/dx.

And a = F/m = F/1 = 8-2x.

adx = vdv. Now, integrate both sides.                                                                                                                                                 The limits of dx will be 0 to 4 and the limits of dv will be 0 to v.

(8x – x^2)0^4 = v^2/2.

∴ v = 4√2 m/s.