A particle is moving along the x -axis under the innuence of a force given by F=-5 x+15. At time t=0, the particle is located at x=6 and is having zero velocity. It takes 0.5 seconds to reach the origin for the first time. The equation of motion of the particle can be represented by

Question

A particle is moving along the x -axis under the innuence of a force given by F=-5 x+15. At time t=0, the particle is located at x=6 and is having zero velocity. It takes 0.5 seconds to reach the origin for the first time. The equation of motion of the particle can be represented by (A) x=3+3 cos π t (B) x=3 cos π t (C) x=3+3 sin π t (D) x=3+3 cos (2 π t)

Tardigrade Admin · Accepted Answer

The mean position of particle can be found by setting

F = - 5 x + 15 = 0

,
so the mean position lies at

x = 3

.
One extreme position is at

x = 6.

Hence the other extreme position for this particle undergoing SHM should be at

x = 0.

Time taken by particle to reach from

x = 6

to

x = 0

is

0.5

second,
that is

T /2 = 0.5 sec

,
hence

T = 1

second.
Hence the equation of motion is

x = 3 + A (sin ω t + ϕ_{0})

where

A = 3, ω = 2 π \times 1

and

ϕ_{0} = \frac{π}{2} .

So

x = 3 + 3 cos (2 π t)

$x = 3 + 3 cos π t$

$x = 3 cos π t$

$x = 3 + 3 sin π t$

$x = 3 + 3 cos (2 π t)$

Q. A particle is moving along the x -axis under the innuence of a force given by F=−5x+15. At time t=0, the particle is located at x=6 and is having zero velocity. It takes 0.5 seconds to reach the origin for the first time. The equation of motion of the particle can be represented by

x=3+3cosπt

x=3cosπt

x=3+3sinπt

x=3+3cos(2πt)

$x = 3 + 3 cos π t$

$x = 3 cos π t$

$x = 3 + 3 sin π t$

$x = 3 + 3 cos (2 π t)$