Finding the Mass Required for Double the Velocity in a Spring-Mass System

[brenfox]

Homework Statement

A mass of 0.3kg is suspended from a spring of stiffness 200Nm. If the mass is displaced by 10mm from its equilibrium position and released for the resulting vibration, calculate:
The mass required to produce double the maximum velocity calculated in question 2 using the same spring and deflection. The velocity in question 2 being 0.26ms-1.

Homework Equations

V=Aωcos(ωt+∅)
ω=√k/m

The Attempt at a Solution

So A=0.01 v= 0.52MS-1.
So transposing ωcos = 0.52/0.01 = 52rads.

Now with these numbers i can find the mass.
ω=√k/m
Transposing m = k/m^2
Mass = 0.07kg.

Now the laws of physics are telling me this answer cannot be right. If an object with a mass of 0.3kg possesses a velocity of 0.26ms-1, then an object with a velocity of 0.52ms-1 should be greater than 0.07kg. The velocity is higher so surely the mass must be greater. Where am i going wrong with this!. Any help would be appreciated.

 

[haruspex]

I see no reason why a greater mass should mean a higher velocity. Think about the acceleration. A higher mass has greater inertia, but the same deflection of the same spring only produces the same force.
Maybe you are subconsciously taking the greater mass case also to have a greater displacement as part of a general scaling up. In that case you could get a greater velocity.