Simple harmonic motion mass on a spring

[saltrock]

A mass is on a spring is pulled down and released.Show thatit performs simple harmonic motion.

as the mass is pulled down and released restoring force pulls it upwards but as it reaches on the top extreme the gravity pulls it down n continuous to oscillate.but how does it prove that motion is SHM??we cannot see acceleration being proportional to the displacement

 

[Integral]

What level of mathematics can you bring to bear?

We know that the total force acting on the mass is

F = -mg-kx

According to Newton this is

ma = -mg-kx

so a = -g - (k/m) x

Does not this show that acceleration is directly proportional to displacement?

 

[Astronuc]

Write the 'equation of motion' of a mass attached to a spring and displaced from equilibrium.

The weight of force of gravity is a constant force which simply displaces the spring from is equilibrium position when there is no mass.

Remember something like - $$m\ddot{x}\,+\,k\,x\,=0$$