Question

In a horizontal block-spring system,the block mass is m=0.5kg and the spring constant is
k =2N/m. At t1=0.1s the block velocity is +0.263m/s and the acceleration is -0.216m/s2. Assuming that the system is undergoing SHM.Write the expression for block displacement from equilibrium point of spring with time

I know we have to find the 3 parameter A, w(angular frequency) and phase

equation : y(t)=Asin(wt+phase)
1.Find angular frequency
w=sqrt(k/m) which is equal to 2rad/s
I really don't know how to find the rest please help me

Answer 1

x= A sin (wt+P
v = Aw cos (wt+P)
a = -Aw^2 sin (wt+P) = -w^2 x

f = m a
-kx = -m w^2 x
so as you probably know
w^2 = k/m

here w^2 = 2/.5 = 4 so w = 2
now
at t = .1
.263 = A(2)cos(.2+P)
-.216 = -A (4)sin (.2+P)

Answer 2

A sin = .054
A cos = .132

sin/cos = tan(.2+P) = .054/.132

inverse tan for .2+P in radians