The pendulum in Figure 1.1(a) swings with a displacement amplitude a. If its start is (a) x= a (b) x= -a find the different values of the phase constant o for the solutions x = a sin (wt + 6)

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1.3
The pendulum in Figure 1.1(a) swings with a displacement amplitude a. If its starting point from rest
is
(a) x= a
(b) x= -a
find the different values of the phase constant o for the solutions
x= a sin (wt + ø)
x = a cos (wt + ø)
x = a sin (wt – o)
x= a cos (wt – 0)
For each of the different values of ø, find the values of wt at which the pendulum swings through the
positions
x= +a/V2
x= a/2
Some Useful Mathematics
31
and
x = 0
for the first time after release from
x = ta
Transcribed Image Text:Problem 1.3 The pendulum in Figure 1.1(a) swings with a displacement amplitude a. If its starting point from rest is (a) x= a (b) x= -a find the different values of the phase constant o for the solutions x= a sin (wt + ø) x = a cos (wt + ø) x = a sin (wt – o) x= a cos (wt – 0) For each of the different values of ø, find the values of wt at which the pendulum swings through the positions x= +a/V2 x= a/2 Some Useful Mathematics 31 and x = 0 for the first time after release from x = ta
(a)
më + mg 4= 0
mx + mg i
ml 0+ mg 0 = 0
w² = g/ I
%3D
mg sin 0 = mg 0
- mg
(m
mg
Transcribed Image Text:(a) më + mg 4= 0 mx + mg i ml 0+ mg 0 = 0 w² = g/ I %3D mg sin 0 = mg 0 - mg (m mg
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