PHYSICS 6B
Ch.12 Worksheet
1) The processing “speed” of a computer refers to the number of binary operations it
can perform in one second, so it is really a frequency. If the processor of a
personal computer operates at 2.50GHz, how much time is required for one
processing cycle?
Period = 1/frequency, so T=1/(2.5x109 Hz)=4x10-10 s.
2) When a 0.22kg air track cart is attached to a spring, it oscillates with a period of
0.84s. What is the force constant for this spring?
𝑇 = 2𝜋
𝑚
2𝜋 2
𝑁
→𝑘=(
) ∙ (0.22𝑘𝑔) = 12.3
𝑘
0.84𝑠
𝑚
3) A mass, m, is attached to a spring of force constant 80.0 N/m and allowed to
oscillate. The figure shows a graph of its velocity as a function of time, t.
·Find the period, frequency, angular frequency and amplitude for this motion.
·At what times between t=0 and t=1.8s does the mass reach maximum displacement
from the equilibrium position?
·Find the magnitude of the maximum acceleration of the mass.
·At what times between t=0 and t=1.8s does the mass reach maximum acceleration
(magnitude)?
·What is the mass, m?
·What is the maximum speed of the mass, and at which times between t=0 and
t=1.8s does it attain that speed?
clas.ucsb.edu/staff/vince/

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
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T=1.6s (peak-to-peak on the graph)
f= 1/T = 0.625 Hz
ω =2πf = 3.93 rad/s
vmax =Aω → A= (0.2 m/s)/(3.93 rad/s) = 0.05 m
max displacement at 0.4s, 1.2s and 2.0s (when v=0)
amax =Aω2 = 0.786 m/s2
max acceleration at 0.4s, 1.2s and 2.0s (when v=0
and displacement is max)

𝜔=

vmax = 0.2 m/s at 0.0s, 0.8s and 1.6s (from graph)
𝑘
𝑚
→𝑚 =
𝑘
𝜔2
= 5.2 𝑘𝑔
PHYSICS 6B
Ch.12 Worksheet
4) When a 0.420 kg mass is attached to a spring, it oscillat es with a period of 0.350s.
If instead a different mass, m2, is attached to the same spring, it oscillates with a
period of 0.700s.
Find (a) the force constant of the spring and (b) the mass of m2.
𝑚
2𝜋
𝑇 = 2𝜋
→𝑘=
𝑘
𝑇
𝑇 = 2𝜋
𝑚
𝑘
→𝑚=
𝑇
2𝜋
2
2
(𝑚) = 135
𝑁
𝑚
(𝑘) = 1.68 𝑘𝑔
Also you could have noticed that the period was
doubled compared to part (a), so the mass should be 4 times as big.
5) When the length of a simple pendulum is tripled, what happens to the period of its
oscillation?
a) The period decreases to 1/3 of the original period.
b) The period does not change.
c) The period increases by a factor of √3.
d) The period increases by a factor of 3.
𝐿
Using 𝑇 = 2𝜋
𝑔
, replace L with 3L and T goes up by factor √3
6) An astronaut notices that a pendulum which took 2.5s for a complete cycle of
swing when the rocket was at rest on the launch pad takes 1.25s for the same
cycle of swing during liftoff. What is the acceleration of the rocket? (Hint: Inside
the rocket, it appears that g has increased.)
Using 𝑇 = 2𝜋
𝐿
𝑔
, since the period is half as big, and the length is the same, gravity
seems 4 times normal. So the rocket must be accelerating upward at 3 times normal
gravity: a rocket=3(9.8 m/s 2) = 29.4 m/s 2
clas.ucsb.edu/staff/vince/