A spring pendulum is a physical system

Physical system

In physics, the word system has a technical meaning, namely, it is the portion of the physical universe chosen for analysis. Everything outside the system is known as the environment, which in analysis is ignored except for its effects on the system. The cut between system and the world is a free...

 where a mass is connected to a spring

Spring (device)

A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication...

 so that the resulting motion contains elements of a simple pendulum as well as a spring. The system is much more complex than a simple pendulum because the properties of the spring adds an extra dimension of freedom to the system. For example, when the spring compresses, the shorter radius causes the spring to move faster due to the conservation of angular momentum

Angular momentum

In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

. Also there is the possibility that the spring has a range that is overtaken by the motion of the pendulum, making it practically neutral to the motion of the pendulum.