Physics 112
Homework #14
Fall 2006
Note: This Homework includes material from Nov 15th to Dec 1
st
and is longer
that the other assignments.
Read:
Chapter 13 (all of it)
For discussion:
Chapter 13:
Qs #Q13.1, Q13.4, Q13.5, Q13.6, Q13.7, Q13.12,
Q13.13, Q13.14, (not turned in)
Q13.15, Q13.16
Chapter 13:
Es & Ps: #13.3, 13.9, 13.17, 13.23, 13.29, 13.31,
13.33, 13.41, 13.49,
13.80, 13.91, 13.95, 13.96
Due Friday, Dec 1
st
at lecture:
#13.16
[Inertia Balance]
#13.19
[Oscillation Function]
#13.27
[Energy in SHM]
#13.45
[Pendulum on Another
Planet]
#13.63
[Block on Block + Spring]
#13.54
[Driven Oscillations]
1.
[SHM Functions & Graphs]
The position as a function of time t for a block
of mass m oscillating on a horizontal ideal spring of spring constant k is x(t) = A
cos(
ω
t).
(a)
Write the oscillator's velocity v(t) and acceleration a(t) in the form C
cos(
ω
t
+
φ
), with C > 0, and find the constants C and
φ
for each function.
(b)
Write the oscillator's kinetic energy K(t) and elastic potential energy U(t) as
functions of time t that are linear in sine or cosine of t. [HINT: The following trig
identities will be useful: sin
2
θ
= (1  cos2
θ
)/2 and cos
2
θ
= (1 + cos2
θ
)/2.]
(c) For
two complete cycles
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 Fall '07
 LECLAIR,A
 mechanics, Simple Harmonic Motion, Work, ad., 0.050 kg, #Q13

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