1.

What units must f( x, t) have in (2.19)?

2.

What are the units of the tension T in the derivation of the wave equation for the string?

3.

What are the units of the parameter c in (2.18)?

4.

Suppose the only external force applied to the string is the force due to gravity. What form does (2.19) take in this case? (Let g be the acceleration due to gravity, and take g to be constant.)

5.

Explain why a homogeneous Neumann condition models an end of the string that is allowed to move freely in the vertical direction.

6.

Suppose that an elastic string is fixed at both ends, as in this section, and it sags under the influence of an external force f( x) ( f is constant with respect to time). What differential equation and side conditions does the equilibrium displacement of the string satisfy? Assume that f is given in units of force per length.

1.

Units of acceleration (length per time squared).

2.

3.

Units of velocity (length per time).

4.

5.

The internal force acting on the end of the string at, say, x = ?, is

If this end can move freely in the vertical direction, force balance implies that (C.1) must be zero.

6.