In Exercise 14.9, let us take the position of mass when the spring is unstreched as x = 0, and the direction from left to right as the positive direction of x-axis. Give x as a function of time t for the oscillating mass if at the moment we start the stopwatch (t = 0), the mass is (a) at the mean position, (b) at the maximum stretched position, and (c) at the maximum compressed position. In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?

Question

Philoid · Accepted Answer

Distance,a = 2 cm,

ω = √k/m

= √1200/3 s^-1

= 20 s^-1

a) As the time is measured from mean position, the phase is 0.

x = a sinωt = 2 sin 20t

b) At the maximum stretched position, the body will be at the extreme right position. The initial phase is π/2.

x = asin (ωt+ π/2) = a cos ωt = 2 cos 20t

c) At the maximum compressed position, the body will be at the extreme left position. The initial phase is 3π/2.

x = asin (ωt+ 3π/2) = -a cos ωt = -2 cos 20t