Question

A particle on a spring moves in simple harmonic motion along the x axis between turning points at x1 = 95 cm and x2 = 135 cm. (i) At which of the following positions does the particle have maximum speed? 95 cm 105 cm 115 cm at none of those positions (ii) At which position does it have maximum acceleration? 95 cm 105 cm 115 cm at none of those positions (iii) At which position is the greatest net force exerted on the particle? 95 cm 105 cm 115 cm at none of those positions

Answer 1

(i)
`x = 115\,cm`, (ii)
`x = 95\,cm`, (iii)
`x = 95\,cm`

Step-by-step explanation:

(i)
`x_(1)` and
`x_(2)` represent the points where particle has a velocity of zero and spring reach maximum deformation, Given the absence of non-conservative force and by the Principle of Energy Conservation, the position where particle is at maximum speed is average of both extreme positions:

`x = 115\,cm`

(ii) Maximum accelerations is reached at
`x_(1)` and
`x_(2)`.

`x = 95\,cm`

(iii) Greatest net forces exerted on the particle are reached at
`x_(1)` and
`x_(2)`.

`x = 95\,cm`