# Scaling factor of a mass spring system

• mrcotton
In summary, if you want to reduce the resonant frequency of a mass spring system to 10Hz, you would need to add 0.60kg to the mass.
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

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

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.

JayneDoe said:
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

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.

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.

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

## What is the scaling factor of a mass spring system?

The scaling factor of a mass spring system is a constant value that determines how much the mass and spring are stretched or compressed. It is typically denoted as k and has units of N/m.

## How is the scaling factor calculated?

The scaling factor is calculated by dividing the force applied to the spring by the resulting displacement of the mass. This can be represented by the equation k = F/x, where F is the force and x is the displacement.

## What happens to the scaling factor if the mass or spring is changed?

If the mass or spring is changed, the scaling factor will also change. This is because the scaling factor is dependent on the properties of the mass and spring, such as their stiffness and mass.

## How does the scaling factor affect the motion of the mass spring system?

The scaling factor affects the motion of the mass spring system by determining the frequency and amplitude of the oscillations. A higher scaling factor leads to a higher frequency and smaller amplitude, while a lower scaling factor leads to a lower frequency and larger amplitude.

## Can the scaling factor be negative?

No, the scaling factor cannot be negative. This is because it represents the stiffness of the spring, which is always positive. A negative scaling factor would indicate that the force applied to the spring is in the opposite direction of the displacement, which is physically impossible.

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