**Simple
Harmonic Motion**

*All amplitudes are in meters, and periods are given in
seconds.*

1) Write an equation for an oscillating spring with an amplitude of 0.15 m and a period of 1.2 seconds.

2) If a 4.5 kg mass bounces on a spring with a period of 1.9 s, what is the spring constant?

3) A spring vibrates according to y = (2.1)sin(0.85t). Find the natural frequency of the spring.

4) An object with a mass of 0.75 kg is attached to an ideal spring described by y = 0.25sin(19t). What is the maximum potential energy of the spring?

5) Using the information given in Question 4, what is the maximum possible speed of the object?

6) If the behavior of a 1.35 kg object attached to a spring is described by y = 0.34sin(0.85t) what is the speed of the object when it is 0.21 m away from the equilibrium position.

7) Imagine a standing wave with a first harmonic vibrating at 440 Hz. If the length of the wire is 0.35 m what is the wave speed along the spring?

8) Another wire, with length 0.55 m, vibrates in its third harmonic. If the speed of the wave is 265 m/s what is the fundamental frequency?