A mass–spring system moves with simple harmonic motion along the x axis between

Question

A mass–spring system moves with simple harmonic motion along the x axis between turning points at x1 = 28 cm and x2 = 81 cm.

A mass-spring system moves with simple harmonic motion along the x axis between turning points at x1 28 cm and x2 81 cm. (i) At which position does the particle have the greatest magnitude of momentum? 28 cm 40.5 cm 54.5 cm O some other position O The greatest value occurs at multiple points. (ii) At which position does the particle have greatest kinetic energy? o 28 cm 40.5 cm 54.5 cm O some other position The greatest value occurs at multiple points. (iii) At which position does the particle-spring system have the greatest total energy? 28 cm 40.5 cm 54.5 cm O some other position The greatest value occurs at multiple points.

Explanation / Answer

i)The maximum momentum will be at the equilibrium position where the speed is maximum.

x = (28 + 81)/2 = 54.5 cm

Hence, x = 54.5 cm

ii)KE will be maximum at equilibrium position.

x = (28 + 81)/2 = 54.5 cm

Hence, x = 54.5 cm

iii)energy is conserved, so

The greatest value occus at multiple points.

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