Question

A particle is moving along the x-axis under the influence 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

• A. $x=3+3cos\pi t$
• B. $x=3cos\pi t$
• C. $x=3+3sin\pi t$
• D. $x=3+3cos\left(2\pi t\right)$

Answer 1

The correct option is D

$x=3+3cos\left(2\pi t\right)$

$F=-5x+15=0$

$x=3$

So, at x = 3, we have equilibrium/ mean position

x = 6 is extreme position

A = 3

T = 1 sec

$\therefore x=3+3cos\left(2\pi t\right)$