CHAPTER 14

1. (P.440 Prob.34) Figure P14.34 is the velocity-versus-time graph of a particle in simple harmonic motion.
   
   a. What is the amplitude of the oscillation?
   b. What is the phase constant?
   c. What is the position at t = 0 s?
2. (P.440 Prob.42) A block on a spring is pulled to the right and released at t = 0 s. It passed x = 3.0 cm at t = 0.685 s, and it passes x = -3.0 cm at t = 0.886 s.
   a. What is the angular frequency?
   b. What is the amplitude?
   Hint: cos(π - θ) = -cosθ.
3. (P.441 Prob.50) A spring with spring constant k is suspended vertically from a support and a mass m is attached. The mass is held at the  point where the spring is not stretched. Then the mass is released and begins to oscillate. The lowest point in the oscillation is 20 cm below the point where the mass was released. What is the oscillation frequency?
4. (P.441 Prob.58) Astronauts on the first trip to Mar's take along a pendulum that has a period on earth of 1.50 s. The period on Mars turns out to be 2.45 s. What is the Martian acceleration due to gravity?
5. (P.442 Prob.72) A 200-g oscillator in a vacuum chamber has a frequency of 2.0 Hz. When air is admitted, the oscillation decreases to 60% of its initial amplitude in 50 s. How many oscillations will have been completed when the amplitude is 30% of its initial amplitude?
6. (P.443 Prob.76) A block on a frictionless table is connected as shown in Figure CP14.76 to two springs having spring constant k₁ and  k₂. Find an expression for the block's oscillation frequency f   in terms of of the frequencies f₁ and f₂ at which it would oscillates if attached to spring 1 or spring 2 alone.