Answer: i dont really get what u are asking but here is what im guessing u mean.
Explanation:Refer to the diagram shown below.
m = 50 g = 0.05 kg, the mass of the ball
A = 6 cm = 0.06 m, the amplitude
The oscillatory motion relative to the equilibrium position is
x(t) = A cos(ωt)
where
x = displacement at time t
A = amplitude, 0.06 m
ω = circular frequency
Therefore
x(t) = A cos(ωt)
The velocity function is
v(t) = - ωA sin(ωt)
The maximum velocity occurs when sin(ωt) = 1. Because the maximum velocity is 3.2 m/s, therefore
(ω 1/s)*(0.06 m) = (3.2 m/s)
w = 53.33 1/s
Therefore
x(t) = 0.06 cos(53.33t)
v(t) = 3.2 sin(53.33t)
When the spring is compressed by 4.5 cm (0.045 m) from the equilibrium position, then
0.06 cos(53.33t) = -0.045
cos(53.33t) = -0.75
53.33t = cos⁻¹ (-0.75) = 2.4189
t = 0.0454 s
The velocity when t = 0.0454 s is
v = 3.2 sin(53.33*0.0454) = 2.111 m/s
The kinetic energy is
KE = (1/2)*m*v²
= 0.5*(0.05 kg)*(2.111 m/s)²
= 0.1114 J
Answer: 0.1114 J
