**Prob. Set 7 due November 9**

**Reading: Ch.6, p. 178 - 196.**

**Exam II: Given out Thur, Nov. 11, due 10am Tues, Nov.16. Covers through
Ch. 5.**

**Problems:**

**1) 6-1**

**2) 6-2**

**3) 6-10**

**4) Find the mode configurations and frequencies for the first three
modes of transverse vibration of a continuous string with tension T _{o},
mass density **m,
and length L given the boundary conditions that

5) The wave machine we used in class consists of a steel wire backbone along the x direction with transverse iron rods. Let k denote the angular spring constant of the wire, i.e. the return torque is k times the angle of twist (in radians). Let I be the moment of inertia of one rod. Find the dispersion relation, i.e. the relation between w and k, for the wave machine.

6) Here are some data for the wave machine:

The rods are 45.7 cm long and 0.40 cm in diameter.

The length of the machine from the first rod to the last rod is 90 cm.

With a 50 gm mass hung 15.3 cm from the wire backbone on rod #1, rod #6 must be twisted by 23.5° to keep rod #1 horizontal.

With the end rods clamped the period measured in class for the n=1 mode was 2.9s, for the n = 2 mode 1.7 s.