Physic help !!!!! Spring problem! Best answer if you help. I need answer ASAP!?

Question

A spring of force constant 210 N/m vibrates with and amplitude of 28 cm when 0.250 kg hangs from it.

a) what is the equation describing this motion as a function of time? assume that mass passes through the equilibrium point with positive acceleration at t=0. b) at what times will the spring have its maximum and minimum extension.

Answer 1

Let the equation is y= A  sin(wt + phi)

At t=0, y= - 0.25 * g / 210 , put the value of g whatever is given

this is -ve as I'm assuming the Y axis origin on the point where the spring would've been if it was placed in a horizontal position. Just turn the whole thing counterclockwise 90 deg to see what i mean.

Now put this value of y to get the value of phase constant phi.

i.e Put A=28(convert into proper unit) and t=0 y as calculated above. Unit of y and A must be same.

Now comes second part.

For maximum extension dy/dt= 0 so

Awcos(wt+phi)=0 that is wt+phi=n*pi/2

Since we know max extension would occur when going down put n=1 , 3 , 5.... to get the value of t basically odd value of n

For minimum extension well y=0!

solve it as above i don remember the general solution when sin=0.

I hope this is correct! :p