MULTIPLE CHOICE

Directions: For each multiple choice problem, choose the answer which is MOST CORRECT. CLEARLY place the letter of your choice in the space provided.

Q1: When the spring constant of a mass-spring system is changed, which of the following is LEAST

affected?

A) the resonant frequency B) the damping C) the period D) the potential energy Answer: ____________

Q2: An object floats with exactly 50% of its volume submerged when placed in salt water, = 1.06 H2O.

When the same object is placed in pure water, what volume is submerged?

A) Still exactly 50% submerged B) Less than 50% submered C) More than 50% submerged D) Cannot be determined without mass Answer: ____________

Q3: A mass-spring oscillator is driven with a periodic force F = Fo cos (wFt). Which of the following

factors does NOT limit affect the maximum possible amplitude of the resulting oscillation?

A) the closeness of wF to the natural frequency wo B) the spring constant k C) mechanical failure of the spring D) the damping constant = b/2m Answer: ____________

Q4: An undamped mass-spring system has a natural frequency o = 3 rad/sec. A small amount of

friction is added to the system, with a damping constant = b/2m = 1 rad/sec. The new oscillation frequency will

A) stay the same, but the oscillation amplitude now decays towards zero B) increase to 4 rad/sec C) slightly increase to 3.2 rad/sec D) slightly decrease to 2.8 rad/sec E) decrease to 2 rad/sec Answer: ____________

The format of the Midterm and Final Exams will be exactly the same as the discussion quizzes you have had. For each problem, you will be given a full page for your work.

PROBLEM A: (25 points)A pulse travels from one end to the other of a long, horizontal string in 0.1 sec. The tension in the string is provided by passing the string over a pulley to a weight which has 100 times the mass of the string.

FIND: What is the length L of the string?

PROBLEM B: (25 points)Professor Collins just barely floats into the sky when tied to 100 large Helium balloons. How many balloons of the same size would be required if they were filled with Neon instead of Helium? Take air = 1.3 kg/m3, He = 0.2 kg/m3, Ne = 0.9 kg/m3. (You may assume that Prof. Collins volume is much, much smaller than the balloons. His mass does not matter, but is probably close to 70 kg.)

FIND: How many Neon balloons will lift Prof. Collins?

PROBLEM C: (25 points)A pendulum with m = 1.0 kg hangs from the end of a massless string having L = 1.0 m. Immediately to the left of its equilibrium point is a spring with spring constant k = 120 N/m. The mass is lifted to an angle = 30o as shown, and then released at t = 0. The pendulum falls down, compresses the spring, and bounces back up to its starting point in a periodic motion. (You may assume that the compression of the spring is approximately linear along x.)

b) FIND: What is the period T of the oscillation? ( Hint: if stuck, maybe begin with a sketch of vs time ) Multiple Choice Solutions: B, C, B, D