There are many examples of SHM. Any body that obeys Hooke’s law and oscillates about an equilibrium point in a periodic motion can be said to be exhibiting SHM. Examples include:
• the tidal motion of water periodically coming in/going out
• a spring oscillating about a point
• a pendulum oscillating (this will be discussed later in the chapter)
• the shadow of a particle undergoing circular motion (Fig. 9.5)
• a block pushed towards a spring on a frictionless surface (Fig. 9.6)
• a tuning fork vibrating. ball v = 0 3 turntable –u 4 screen
FIG. 9.5 The shadow projected by the ball will oscillate across the screen with SHM
m
motion of paper
FIG. 9.7 In this experiment, the paper rolls by as the spring vibrates up and down. In doing this, it draws a characteristic periodic sine wave formation
In Fig. 9.6:
1. A block moving with constant velocity u impacts a spring. 2. The block changes to a velocity v as it begins to slow down with the spring resistance.
3. The block stops and its velocity is now zero but it has maximum potential energy.
4. The spring rebounds the block with equal restoring force and causes the block to return to the original speed but opposite direction (−u).
Fig. 9.7 shows how a spring undergoing SHM draws a sine-wave shape if a pencil is attached to it. (You will study these waveforms in more detail in Chapter 16.)
86 FUSION
FIG 9.6 The moving block initially compresses the spring. This will cause the spring to undergo SHM, much like the vertical spring
___ m to find w.
Frequency and period are related as follows:
Periodic time T = 1
__ f
T = period (s), f = frequency of oscillation (Hz)
You also need to know this formula, although no derivation is required: T = 2o
____ v
T = period (s), w = constant
As the ball rotates with uniform motion in Fig. 9.5, the shadow that it projects moves over and back with SHM.
