15 • Oscillatory Motion - ECHSPhysics

15.3 (a). The amplitude is larger because the curve for Object
B shows that the displacement from the origin (the vertical
axis on the graph) is larger. The frequency is larger
for Object B because there are more oscillations per unit
time interval.
15.4 (a). The velocity is positive, as in Quick Quiz 15.2. Because
the spring is pulling the object toward equilibrium from
the negative x region, the acceleration is also positive.
15.5 (b). According to Equation 15.13, the period is proportional
to the square root of the mass.
15.6 (c). The amplitude of the simple harmonic motion is the
same as the radius of the circular motion. The initial position
of the object in its circular motion is radians from
the positive x axis.
15.7 (a). With a longer length, the period of the pendulum will
increase. Thus, it will take longer to execute each swing,
so that each second according to the clock will take
longer than an actual second—the clock will run slow.
Answers to Quick Quizzes 485
15.8 (a). At the top of the mountain, the value of g is less than
that at sea level. As a result, the period of the pendulum
will increase and the clock will run slow.
15.9 (a). If your goal is simply to stop the bounce from an absorbed
shock as rapidly as possible, you should critically
damp the suspension. Unfortunately, the stiffness of this
design makes for an uncomfortable ride. If you underdamp
the suspension, the ride is more comfortable but the
car bounces. If you overdamp the suspension, the wheel is
displaced from its equilibrium position longer than it
should be. (For example, after hitting a bump, the spring
stays compressed for a short time and the wheel does not
quickly drop back down into contact with the road after
the wheel is past the bump—a dangerous situation.) Because
of all these considerations, automotive engineers
usually design suspensions to be slightly underdamped.
This allows the suspension to absorb a shock rapidly (minimizing
the roughness of the ride) and then return to equilibrium
after only one or two noticeable oscillations.