Transcript College Physics - Gianpietro Cagnoli's Homepage

Chapter 12 – part C
The Physical Pendulum
Damped Oscillations
Forced Oscillations
In-phase and quadrature
components of motion
In-Phase
Interesting properties:
Quadrature
The forced and damped
harmonic oscillator
For X:…
For Y:…
From the last one and considering the relation between sin and cos:
From the X equation, one can work out A:
Replacing cos j and sin j:
Exercise 12.28
28.
A very light rigid rod with a
length of 0.500 m extends straight out
from one end of a meter stick. The stick
is suspended from a pivot at the far end
of the rod and is set into oscillation.
(a) Determine the period of oscillation.
(b) By what percentage does the period
differ from the period of a simple
pendulum 1.00 m long?
Exercise 12.31
31.
A pendulum with a length of 1.00
m is released from an initial angle of
15.0°. After 1 000 s, its amplitude has
been reduced by friction to 5.50°. What is
the value of b/2m?
Exercise 12.31
33.
A 2.00-kg object attached to
a spring moves without friction and
is driven by an external force
F = (3.00 N) sin(2πt). Assuming that
the force constant of the spring is
20.0 N/m, determine (a) the period
and (b) the amplitude of the motion.
Exercise 12.24
24.
The angular position of a
pendulum is represented by the equation
θ = (0.032 0 rad) cos ωt, where θ is in
radians and ω = 4.43 rad/s. Determine the
period and length of the pendulum.
Exercise 12.36
36.
Damping is negligible for a
0.150-kg object hanging from a light
6.30-N/m spring. A sinusoidal force with
an amplitude of 1.70 N drives the
system. At what frequency will the force
make the object vibrate with an
amplitude of 0.440 m?
Exercise 12.49
49.
A horizontal plank of mass m and
length L is pivoted at one end. The plank’s
other end is supported by a spring of force
constant k. The moment of inertia of the
plank about the pivot is . The plank is
displaced by a small angle θ from its
horizontal equilibrium position and
released. (a) Show that it moves with
simple harmonic motion with an angular
frequency   3k / m .
(b) Evaluate the frequency, assuming that
the mass is 5.00 kg and that the spring has
a force constant of 100 N/m.