The angular displacement θ (in radians) for a simple pendulum is given by θ = 0.175 sin π t . a. Determine the period of the pendulum. b. How many swings are completed in 1 sec ? c. To the nearest degree, what is the maximum displacement of the pendulum? d. The length L of a pendulum is related to the period T by the equation T − 2 π L g , where g is the acceleration due to gravity. Find the length of the pendulum to the nearest meter g = 9.8 m / s e c 2 .
The angular displacement θ (in radians) for a simple pendulum is given by θ = 0.175 sin π t . a. Determine the period of the pendulum. b. How many swings are completed in 1 sec ? c. To the nearest degree, what is the maximum displacement of the pendulum? d. The length L of a pendulum is related to the period T by the equation T − 2 π L g , where g is the acceleration due to gravity. Find the length of the pendulum to the nearest meter g = 9.8 m / s e c 2 .
Solution Summary: The author calculates the period of the pendulum and the number of swings completed in 1sec.
The angular displacement
θ
(in radians) for a simple pendulum is given by
θ
=
0.175
sin
π
t
.
a. Determine the period of the pendulum.
b. How many swings are completed in
1
sec
?
c. To the nearest degree, what is the maximum displacement of the pendulum?
d. The length
L
of a pendulum is related to the period
T
by the equation
T
−
2
π
L
g
, where
g
is the acceleration due to gravity. Find the length of the pendulum to the nearest meter
g
=
9.8
m
/
s
e
c
2
.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)
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