A Classical Approach of Newtonian Mechanics

11 OSCILLATORY MOTION 11.2 Simple harmonic motion

ω t − φ 0 ◦^90 ◦ 180 ◦ 270 ◦

x +a

0

−ω^2 a

0

−ω a

0

−a

0

+ω^2 a

0

+ω a

0

x ̇

x ̈

Table 4: Simple harmonic motion.

Figure 95: Simple harmonic motion.

It can be seen that ω is the motion’s angular frequency (i.e., the frequency f

converted into radians per second). Finally, the phase angle φ determines the

times at which the oscillation attains its maximum amplitude, x = a: in fact,

Here, n is an arbitrary integer.

tmax = T n +

φ

2 π

!. (11.8)

Table 4 lists the displacement, velocity, and acceleration of the mass at various

phases of the simple harmonic cycle. The information contained in this table can

easily be derived from the simple harmonic equation, Eq. (11.3). Note that all

of the non-zero values shown in this table represent either the maximum or the

minimum value taken by the quantity in question during the oscillation cycle.

We have seen that when a mass on a spring is disturbed from equilibrium it