A 0.520 kg object connected to a light spring with a spring constant of 22.0 N/m

Question

A 0.520 kg object connected to a light spring with a spring constant of 22.0 N/m oscillates on a frictionless horizontal surface. ALL OF A,B,& C ARE CORRECT. JUST NEED HELP WITH :For what values of x is the speed of the object 0.15 m/s?
x = ±  cm

(a) Calculate the total energy of the system and the maximum speed of the object if the amplitude of the motion is 3.00 cm.

(b) What is the velocity of the object when the displacement is 2.00 cm?
± 0.45 m/s

(c) Compute the kinetic and potential energies of the system when the displacement is 2.00 cm.

THIS IS WHAT I NEED HELP WITH:

For what values of x is the speed of the object 0.15 m/s?
x = ±  cm

Explanation / Answer

angular frequency=sqrt(spring constant/mass)=6.5044 rad/sec

the position can be written as

x=0.03*sin(6.5044*t)

velocity=dx/dt=0.1951*cos(6.5044*t) m/s

so for velocity to be 0.15 m/s

0.15=0.1951*cos(6.5044*t)

t=0.1067 seconds

then x=0.03*sin(6.5044*0.1067)=0.0192 m=1.92 cm

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