What happens when you drop a mass on an oscillating spring?

The dropped mass collides inelastically with the oscillating mass. They stick together and oscillate at a lower frequency with a new equilibrium position. Momentum is conserved but kinetic energy is lost.

Why does the frequency decrease after the collision?

The frequency of a spring-mass system is omega equals square root of k over m. When the mass increases from m1 to m1 plus m2 the frequency decreases because the denominator is larger.

Dropping a Mass on an Oscillating Mass — In...

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Dropping a Mass on an Oscillating Mass