Hookes Law and Simple Harmonic Motion
Physics 1405 Name(s)_____________________
HOOKE’S LAW and SIMPLE HARMONIC MOTION
INTRODUCTION
Any motion that repeats itself in equal intervals of time is called periodic motion. A special form of periodic motion is called Simple Harmonic Motion (SHM). Simple Harmonic Motion is defined as oscillatory motion in which the resultant force on the oscillating body at any instant is directly proportional to its displacement from the rest position and opposite in direction to its motion.
For a spring system, this can be written as F = -kx where F is the resultant force on the object attached to the spring, x is the displacement of the object from equilibrium and k is a constant called the spring constant. The force is a restoring force because it tends to restore the object back to its original position. This relationship is called Hooke’s Law.
If a mass is attached to a spring and then displaced from its rest position and released, it will oscillate around that rest position in simple harmonic motion. The period T of the oscillating system does not depend on the displacement from rest as long as the spring is not overstretched. The period is the time it takes for as system to go through one full oscillation and return to its starting position.
In this lab we will study Hooke’s Law for a mass connected to a spring and then investigate the SHM of the mass on the spring. We will find the spring constant in each case and compare the results.
Part I. HOOKE'S LAW
PROCEDURE
1. Mount the spring so that it hangs vertically. Attach a mass hanger or a small mass and allow the system to stretch to an equilibrium state (the x = L situation in the figure).
[pic]
2. Place the bottom of the mass hanger or small mass even with a reference point on a meter stick as shown in the figure. This will be your zero for measurements.
[pic]
3. Now, add masses in units of about 50 g up to a total of about 250 g.
HOOKE’S LAW and SIMPLE HARMONIC MOTION
INTRODUCTION
Any motion that repeats itself in equal intervals of time is called periodic motion. A special form of periodic motion is called Simple Harmonic Motion (SHM). Simple Harmonic Motion is defined as oscillatory motion in which the resultant force on the oscillating body at any instant is directly proportional to its displacement from the rest position and opposite in direction to its motion.
For a spring system, this can be written as F = -kx where F is the resultant force on the object attached to the spring, x is the displacement of the object from equilibrium and k is a constant called the spring constant. The force is a restoring force because it tends to restore the object back to its original position. This relationship is called Hooke’s Law.
If a mass is attached to a spring and then displaced from its rest position and released, it will oscillate around that rest position in simple harmonic motion. The period T of the oscillating system does not depend on the displacement from rest as long as the spring is not overstretched. The period is the time it takes for as system to go through one full oscillation and return to its starting position.
In this lab we will study Hooke’s Law for a mass connected to a spring and then investigate the SHM of the mass on the spring. We will find the spring constant in each case and compare the results.
Part I. HOOKE'S LAW
PROCEDURE
1. Mount the spring so that it hangs vertically. Attach a mass hanger or a small mass and allow the system to stretch to an equilibrium state (the x = L situation in the figure).
[pic]
2. Place the bottom of the mass hanger or small mass even with a reference point on a meter stick as shown in the figure. This will be your zero for measurements.
[pic]
3. Now, add masses in units of about 50 g up to a total of about 250 g.