1. ## Period of Oscillation

Kindly help me with the following question.
A particle of unit mass performing (lightly) damped simple harmonic oscillations satisfies - kx - a x' = x'' three consecutive postions of instantaneous rest, relative to origin O, are given x=6, x=3, x=4 at approximately equal intervals of 2 seconds. Find period of oscillation for the undamped oscillator.
thanks

2. Originally Posted by charikaar
Kindly help me with the following question.
A particle of unit mass performing (lightly) damped simple harmonic oscillations satisfies - kx - a x' = x'' three consecutive postions of instantaneous rest, relative to origin O, are given x=6, x=3, x=4 at approximately equal intervals of 2 seconds. Find period of oscillation for the undamped oscillator.
thanks
Sketch the graph of lightly dammed SHM, look at three consecutive points where the particle is stationary (horizontal tangent).

These three points will be close to stationary points for the for undamped SHM and so can be used to estimate the period of the undamped SHM.

.

3. Thanks for that.

to draw a graph x(t) is on the vertical axis and t is on horizental axis? is t in seconds or radians? sorry if i sound too stupid but do you know what t=? when particle is at instantaneous rest. I know the solution is x(t)=acos(wt-\$)

instantaneous rest when x'(t)=0 what is the positions of instantanaeous rest?