Motion of a Particle Attached to Two Springs on a Smooth Surface
A particle between two springs on a table can execute simple harmonic motion if pulled to one side.
A particle of mass m is attached to two strings of natural lengthsandand force constantsandrespectively. The ends of the springs are attached to endpoints A and B, so thatand both springs are initially in tension. Suppose that the mass is pulled to the right from its equilibrium position so that the length of spring 1 isand the length of spring 2 is
The tension in spring 1 isand the tension in spring 2 is
The resultant force on the mass isUsinggives
When the system is in equilibrium,so that
LetthenandSubstitute this into (1) to give
Henceand the motion is simple harmonic with period