A 2g block attached to an ideal spring with a spring constant of 80N/m oscillates on a horizontal frictionless surface.When the spring is 4.0 cm shorter than its equilibrium length,the speed of 17^1/2m/s.The greatest speed of the block is

1)4m/s

2)6m/s

3)5m/s

4)9m/s

5)3m/s

This is SHM.

k = 80 N/m m = 0.002kg
ω = angular frequency of SHM of spring mass system
=> ω² = k/m = 80/0.002 => ω = 200 rad/sec²

Let the equation of SHM be: x = x₀ Sin (200 t)
and v = x₀ * 200 Cos( 200 t)

Given that displacement 0.04 meters = x₀ Sin(200 t)
and speed: √17 m/s = x₀ 200 * Cos (200t)

Hence, 0.04² + (√17/200)² = x₀²
x₀ = 0.0449m or 4.499cm

Thus the maximum speed of the block = x₀ * ω
=0.0449×200
= 8.98 m/sec
=9m/s