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

The mean position of particle can be found by setting F = -5x + 15 = 0, so the mean position lies at x = 3. One extreme position is at x:6. Hence the other extreme positionfor this particle undergoing SHM should be at x = 0. Time taken by particle to reach from x=6 to r - 0 is 0.5 second, that is, T/2=0.5 sec, hence T=1 second. Hence the equation of motion is x=3+Asin⁡ωt+ϕ0) where A=3,ω=2π×1 and ϕ0=π2. So x=3+3cos⁡(2πt)