Download Physics PHYS 250/251 Dynamics/Mechanics I Problem Set #1

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Physics PHYS 250/251
Dynamics/Mechanics I
Problem Set #1
Topics Covered:
Vectors
Scalar products
1.
2.
r
r r
r
For the vectors A and B if A = 5iˆ + 2 ˆj − 6kˆ and B = 3iˆ − ˆj + 4kˆ ,
a)
find the direction cosines of each vector.
b)
find the scalar product.
c)
find the angle between the two vectors
i)
using the scalar product.
ii)
using the direction cosines
d)
find the cross product using
i)
direct multiplication.
ii)
a determinant.
Consider the differential equation
a)
b)
3.
Cross products
Differential Equations
dz
+ 5 z = sin x .
dx
Solve for the initial condition z (0) = 12 using the integrating factor
technique.
Check your answer.
Solve the following differential equation for the initial conditions y (0) = 0 and
y (3) = 1.
3
d2y
dy
− 12
+ 6 y = t 2 sin ωt .
2
dt
dt
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