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October 30.doc
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McGill University
Physics
PHYS 101
Kenneth Ragan
Fall
Description
Phys 101 Alanna Houston
October 30, 2007
 Hooke’s Law: F = kx
 x = 0 is the equilibrium position
 +ve x is towards extension
 Force is always opposite displacement so it works to bring back
object (always a restoring force)
 Motion through one complete cycle, starting from a compressed
and motionless state:

 When x is at equilibrium position, then speed is maximum and F is
0
 Motion is Periodic and oscillatory: simple harmonic motion (SHM)
 In SHM or an SHO, F ~ x
 T is time for one complete motion related to frequency by T = 1/f
 Since force is always changing, so is acceleration therefore you
CANNOT use constant accelerations formula
 Instead you have to use energy formulae.

 Last one for frictionless surface Phys 101 Alanna Houston
 The total energy in a system is proportional to the square of the
amplitude of the oscillation
 At equilibrium:
 In general, at any arbitrary point:

 Example: When a spring stretches 0.150m when a 0.300 kg mass
is lowered GENTLY on it. Spring is then set up horizontally with the
same mass on a frictionless table, and pulled 0.100 m from the
equilibrium point. Find a)k, b)A, c)vmax, d)v when mass is 0.050 m
from equilibrium, e)amax
o A) mg = kx when x = 0.250 m. Therefore, k = 19.6 N/m.
o B) A = 0.100 m
o C) Vmax = Asqrt(k/m) = 0.1(sqrt(19.6/0.3)) = 0.81 m/s
o D) v = Vmax(sqrt(1x^2/A^2)) = 0.81*sqrt(1
(0.05/0.1)^2)= 0.7 m/s
o E) amax = kx, when x is max…at two max points. Therefore,
amax = kA/m. amax = 19.6*0.1*0.3 = 6.5 m/s^2
 To look at period of simple harmonic motion, use uniform circular
motion viewed from the side
 Phys 101
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