Finding Mass in SHM with Known Spring Constant and Velocity

[JoulesVerms]

Homework Statement

A block of unknown mass is attached to a spring with a spring constant 9.00 N/m and
undergoes simple harmonic motion, along the x axis, with an amplitude of 10.0 cm. When the
mass is halfway between its equilibrium position and its maximum positive displacement, its
velocity is measured to be +30.0 cm/s. Calculate
(a) the mass of the block,

Homework Equations

??

The Attempt at a Solution

I tried using the x= A cos (ωt +∅) but i can't figure it out without time. HELP?? I know the answer is suposed to be m= 0.750kg but i don't understand how to get there.

 

[ehild]

What is cos(ωt +∅) when the mass is halfway between its equilibrium position and its maximum positive displacement?

What is the formula for velocity as function of t?
How is ω related to mass?

ehild

 

[azizlwl]

Since OP not interested, i find the problem interesting since i just started on SHM.

Using circular motion method.
Since position is halfway between its equilibrium position and its maximum positive displacement,
θ=60°
V_maxCos(90-θ)=0.3 m/s
V_max=0.3x 2/√3

F=mv²/r
m=0.9 x 0.1 x 3/(0.36)
m=0.75 kg