Lab B1 Simple Harmonic Motion.docx - Lab B1 Simple Harmonic...

Lab B1: Simple Harmonic Motion
Objectives
1. To determine the spring constant k by stretching the spring and applying Hooke’s Law
2. To verify that the period of vibration of a body on a spring is independent of the
amplitude, and is given by T =
2 π
√
m / k
3. To measure the period T of a simple pendulum as a function of the length L of the
pendulum, and to verify that it is given by T =
2 π
√
L / g
Background
When a body of mass m is suspended on a coil spring with spring constant k, and if the spring is
stretched or compressed from its equilibrium position through a displacement s, the spring exerts
on the body a force that is proportional to the displacement and given by Hooke’s Law
⃗
F =− k ⃗ s
of which magnitude F = ks
We call F a restoring force. The negative sign indicates that the force direction is opposite to the
direction of the displacement. If the spring is hung vertically, when the body is stationary,
according to Newton’s First Law we know that F = mg so therefore mg = ks
Procedure
Part 1
1. With the lab equipment provided in the counter tray, clamp a one- or two- meter stick in a
vertical position. Hang the spring at the groove of the rod and carefully record the
position y
o
of the bottom of the spring. Then hang the 50g weight hanger at the bottom of
the spring.
2. Add 100g weight to the weight hanger and record the position y
1
of the bottom of the
spring.
3. Add more weight to the weight hanger, and record in Data Table 1 the position y
1
of the
bottom of the spring for each added weight.