Question
In Exercise 14.9, let us take the position of mass when the spring is unstretched 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?
Solution
Distance travelled by the mass sideways, a = 2.0 cm
Angular frequency of oscillation,
Angular frequency of oscillation,
(a)
As time is noted from the mean position, hence using
As time is noted from the mean position, hence using
x = a sin ω t, we have x = 2 sin 20 t
(b)
At maximum stretched position, the body is at the extreme right position, with an intial phase of π/2 rad.
Then,
At maximum stretched position, the body is at the extreme right position, with an intial phase of π/2 rad.
Then,
(c) At maximum compressed position, the body is at left position, with an initial phase of 3 π/2 rad.
Then,
Then,
The functions neither differ in amplitude nor in frequency.
They differ in initial phase.
They differ in initial phase.
