Reading HW 1

Question 1

What are the 5 powerful Math Techniques

Answer 1

Substitution
Taylor Series Expansion
Product Rule/Integration by Parts
Logarithmic Differentiation
Garrets first law of Geometry

Question 2

If the second derivative of a function is positive, the curvature of the function is ________?

Answer 2

upwards

Question 3

If the second derivative of a function is negative, the curvature of the function is _______?

Answer 3

downwards

Question 4

What two types of mathematical expressions is logarithmic differentiation most useful for?

Answer 4

1. Products

2. Exponents

Question 5

What 3 conditions must be true to satisfy Hooke’s law?

Answer 5

1. The vector sum of all the forces acting on a body must be equal to ZERO
2. The first derivative of an objects potential energy with respect to position must be ZERO
3. The second derivative of an objects potential energy must be positive

Question 6

What is the condition that needs to be met in order for Hooke’s Law to remain true?

Answer 6

The displacements from equilibrium must be relatively small… dx/x0 &laquo_space;1

Question 7

For linear systems that obey Hooke’s law, the frequency of the oscillation is independent of the ______?

Answer 7

amplitude

Question 8

The _______ response of the system to a driven force occurs only at the ________

Answer 8

steady state

driving frequency

Question 9

What is a point mass? How does it move in 1 DOF?

Answer 9

A mass where you neglect the spacial distribution

It moves only along 1 axis

Question 10

What is the dynamical equation?

Answer 10

Newtons second law of motion… a force acting upon an object causes it to accelerate according to the formula net force = mass x acceleration. So the acceleration of the object is directly proportional to the force and inversely proportional to the mass.

Question 11

What is the equation of state for a mass-spring system?

Answer 11

second order, homogeneous, linear differential equation

Question 12

Two springs connected in parallel will both have the same _______ and the total combined spring constant will be the _______ of the individual stiffnesses.

Answer 12

Displacement

Sum

Question 13

Two springs connected in series will have the same ___________ and the effective spring constant will be _________ than either spring acting alone.

Answer 13

forces at X0

less

Question 14

For a mass-spring system, where the mass of the spring is much less than the point mass attached at the end of the spring, what fraction of the spring mass should be included in the total mass of the system?

Answer 14

1/3 of the springs mass should be included in the mass of the system