Question

Lab 11. Simple Harmonic Motion

Introduction

Lots of things vibrate or oscillate. A vibrating tuning fork, a moving child’s playground swing, and the speaker in a headphone are all examples of physical vibrations. There are also electrical and acoustical vibrations, such as radio signals and the sound you get when blowing across the top of an open bottle. Adding heat to a solid increases the vibration of atoms and molecules. One simple system that vibrates is a mass hanging from a spring. The force applied by an ideal spring is proportional to how much it is stretched or compressed. Given this force behavior, the up and down motion of the mass is called simple harmonic and the position can be modeled with

y = Asin(2πft +ф)

In this equation, y is the vertical displacement from the equilibrium position, A is the amplitude of the motion, f is the frequency (number of oscillations per second), t is the time, and ф is a phase constant that tells us the value of y at t = 0. This experiment will clarify each of these terms. The frequency where k is the spring constant and m is the mass.

Objectives

• Measure the position and velocity as a function of time for an oscillating mass and spring system.
• Determine the amplitude, period, and phase constant of the observed simple harmonic motion.
• Compare the observed motion of a mass and spring system to a mathematical model of simple harmonic motion.

Task:

          Complete the tables

          Analysis Part 1: #3&4

          Extension: #6

3. Does the frequency, f, appear to depend on the amplitude of the motion? Do you have enough data to draw a firm conclusion?

4. Does the frequency, f, appear to depend on the mass used? Did it change much in your tests?

6. Did the introduction of damping have a significant effect on the frequency? On the damping coefficient?

Data Tables

Run	Mass (g)	y0 (m)	A(m)	t(s)	f (hz)
1	200	.333	.05	.722
2	200	.333	.1	.724
3	300	.5	.05	.877

Find the spring constant: k=                            

	Time (s)	Position (m)
When v=0	.248
When v=max	.597

Ф=3.708

Fitted equation with parameters for run 3: y = A*sin(2πft + ф) + y0

Effect of damping
	Damping coefficient (s-1)	Frequency (Hz)
With damping	.1393	1.124
Without damping	0	1.138

Answer 1