Scaling factor of a mass spring system

[mrcotton]

Homework Statement

A mass spring system carries a mass of 0.4kg. When the point of suspension is made to vibrate verticaly at a frequency of 15Hz resonance occurs. What mass should be added to the 0.4kg in order to reduce the resonant frequency to 10Hz.

a) 0.20kg
b) 0.40kg
c) 0.50kg
d) 0.60kg

Homework Equations

T=2∏√(m/k)
15=2∏√(0.4/k)

The Attempt at a Solution

15=2∏√(0.4/k)
10=2∏√(0.4+x/k)

Do I rearrange these so I have all the constants on the rhs then equate the lhs and solve for x if that makes sense?
Any help appreciated

 

[JayneDoe]

It wouldn't really make sense to try to 'put all the constants on the RHS of the equation' - everything in the first equation is a constant and we know that 'x', the only variable in the second equation, cannot be zero.

Consider, instead, that 'k', as a property of the spring, will not change between the two scenarios.

EDIT: Oh, and 'T' represents the period of oscillation rather than the frequency.

 

[mrcotton]

It wouldn't really make sense to try to 'put all the constants on the RHS of the equation' - everything in the first equation is a constant and we know that 'x', the only variable in the second equation, cannot be zero.

Consider, instead, that 'k', as a property of the spring, will not change between the two scenarios.

EDIT: Oh, and 'T' represents the period of oscillation rather than the frequency.

I just realized the T=1/f mistake
Thanks for the help

 

[mrcotton]

0.06=2∏√(0.4/k)
0.1=2∏√(0.4+x/k)

So I still can't seem to get 0.5 out of the rearrangement and equation of the two formula.

 

[JayneDoe]

I'm able to get x=0.5kg by that method, actually. If you leave '1/15' on the LHS of the first equation rather than approximating it as '0.06', you should find the same.

 

[mrcotton]

Thanks for the help,
I love the techniques of physics.
I got lost in the algebra