Spring constant problem. what is the formula for k in terms of the period t and the mass? A sping-mass system is composed of a massless spring with one end fixed to a rigid support and a mass attached to the end (which is free to move). This system performs simple harmonic motion under the restoring force of the spring. The period/frequency of a simple harmonic motion depends on the factors that affect the restoring force and the inertia of the system. For a spring-mass system, these factors are the spring constant and the mass attached to the spring. The period of a spring-mass system is given by the following equation:T=2π√mKHere,m is the mass attached to the oscillating end of the spring.K is the spring constant.The spring constant can be expressed in terms of the period and mass by rearranging the above equation as:T2=(2π√mK)2⇒T2=4π2mK⇒K=4π2mT2