As it turns out, a pendulum is a simple harmonic oscillator as well...its accele

Question

As it turns out, a pendulum is a simple harmonic oscillator as well...its acceleration is directly (negatively) proportional to its displacement from equilibrium.  We'll actually do the physics of proving that in our next lecture.  For now, some of the results in section 13.4 of you text will be useful.

A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor and that its period is 27.0 s.

x = (0.30 m) cos(?t/3)

Explanation / Answer

a) T = 2*pi*sqrt(L/g)

L = g*T^2/(4*pi^2)

= 9.8*27^2/(4*3.14^2)

= 181.15 m

b)

Tm/Te = sqrt(ge/gm)

Tm = Te*(sqrt(9.8/1.67))

Tm = 65.4 s


2)


a) x = 0.3*cos(pi*t/3)


at t = 0, x = 0.3 m

at t = 0.4, x = 0.274 m

b)

A = 0.3 m

c)

w = pi/3

2*pi*f = pi/3


f = 1/6 = 0.167 hZ

d) T = 1/f = 6 s

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