Question

A particle performs S.H.M. of period 24 s. Three second after passing through the mean position it acquires a velocity of 2 π m/s. Its path length is ______.

`(sin45^circ=cos45^circ=1/sqrt2)`

Options

• `24sqrt2  "m"`

• `48sqrt2  "m"`

• `36sqrt2  "m"`

• `12sqrt2  "m"`

Answer 1

A particle performs S.H.M. of period 24 s. Three second after passing through the mean position it acquires a velocity of 2 π m/s. Its path length is `underline(48sqrt2  "m")`.

Explanation:

T = 24 s

`therefore omega=(2pi)/T=(2pi)/24=pi/12  "rad/s"`

v = 2π m/s at t = 3

v is given by v = Aω cos ωt

`therefore2pi=Axxpi/12xxcos  pi/12*3`

`therefore24=Acos  pi/4`

`therefore24=A*1/sqrt2`

`thereforeA=24sqrt2  "m"`

Path length = 2A = `48sqrt2  "m"`