The period (T ) of a particle executing SHM is the time taken for one complete oscillation.
The period is equal to the inverse of the frequency (f ). The period for SHM can also be related to angular frequency in the same formula as for circular motion, i.e.
T 2p v
PERIOD
T periodic time,v angular frequency T 2p
v Systems that Obey Hooke’s Law
Execute SHM When a body that obeys Hooke’s law is oscillating, it executes simple harmonic motion. Based on Newton’s second law and Hooke’s law we get: F ma & F ks
a
ma ks k
m s
(this implies a s, which implies the body is undergoing SHM).
r Equating this with the definition of SHM we get:
v2 s k m s
v2 k m
v Am k
divide both sides by s square root both sides
In questions involving the calculation of the elastic constant, once it is calculated it can be used to find the constant of proportionality or angular frequency when the spring is executing SHM. It is important to note that the being mass referred to when applying the formula to calculate angular frequency may be different to the mass used to calculate the value of the elastic constant.
SAMPLE PROBLEM 7A Calculate the value of the elastic constant k for a spring that is compressed 6 mm by a mass of 90 kg.
SIMPLE HARMONIC MOTION AND HOOKE’S LAW 113 v Am
ANGULAR FREQUENCY k
v angular frequency k elastic constant m mass
