When the spring comes to rest, the force down due to weight down is equal (in magnitude) to the restoring force up due to the elastic properties of the spring. Weight mg 90 9.8 882 N Restoring force 882 N
mg 882
882 ks 882 k (6 103)
The elastic constant has a value of 1.47 105 N m1. k 882
SAMPLE PROBLEM 7B
A mass of 400 g is hung from a spring, causing an extension of 20 cm; calculate the elastic constant of the spring.The 400 g mass is replaced by a 300 g mass and this is then pulled down a small distance past its equilibrium position and allowed to oscillate up and down. Calculate the frequency of oscillation, accurate to two significant figures.
SAMPLE ANSWER 7B Using the formula for elastic constant, making sure all values are in their standard unit:
k The elastic constant is 19.6 N m1.
Using the formulae for angular frequency and simple harmonic motion, making sure all values are in their standard unit:
v Am A k
19.6 0.3 8.08
T 2p v 2p
f 1 T 1
The frequency of oscillation is 1.3 Hz. DEMONSTRATION 7.1
Demonstration of Simple Harmonic Motion Apparatus Motion sensor, data logger and calculator, Newton weights, retort stand and clamp, spring
