Displacement in simple harmonic motion

[Dragoon]

i have a problem i am working on and i am just not sure how to do it i was looking for some help i will state the problem then explain the way i am trying to do it. thanks for any help in advance.

A 0.27 kg mass is suspended on a spring that stretches a distance of 4.9 cm. The mass is then pulled down an additional distance of 12.5 cm and released. What's the displacement from the equilibrium position with the mass attached (in cm) after 0.42 s? Take up to be positive and use g = 9.81 m/s2.

i think the equation for such a problem is Y(t)=-ACosWT
but all i have is a mass distance and distance the spring stretches i need to find the spring constant and the amplitude then i think i can solve this problem but i am not sure can anyone help?

 

[James R]

If the mass stretches the spring by 4.9 cm, then

$$mg = kx$$

This let's you calculate k, the spring constant.

The angular frequency is then:

$$\omega = \sqrt{k/m}$$

 

[Dr Transport]

assume that the mass moves in a sinusoidal motion $$A\sin(\omega t)$$ where $$A$$ is the initial displacement.