# Natural angular frequency

## Homework Statement

The suspension of a modified baby bouncer is modelled by a model spring AP with stiffness k1 and a model damper BP with damping coefficient r. The seat is tethered to the ground, and this tether is modelled by a second model spring PC with stiffness k2.

The bouncer is suspended from a fixed support at a height h above the floor.

Determine the natural angular frequency of the system to two decimal places.

Values of k1, k2 and m are given.

## Homework Equations

1. I know natural angular frequency ω = √(k/m)

## The Attempt at a Solution

With one fixed spring, I can find ω, but not sure what happens with two fixed springs. I tried adding k1 and k2 together, but got an integer answer that requires no rounding.

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BvU
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to two decimal places.
Can't be done with the given information. You sure this is the actual, complete problem statement ?

The full problem statement is as follows:

The suspension of a modified baby bouncer is modelled by a model spring AP with stiffness k1 and a model damper BP with damping coefficient r. The seat is tethered to the ground, and this tether is modelled by a second model spring PC with stiffness k2. Model the combination of baby and seat as a particle of mass m at a point P that is a distance x above floor level.

The bouncer is suspended from a fixed support at a height h above the floor. The suspending spring has natural length l1, while the tethering spring has natural length l2. Take the origin at floor level, with the unit vector i pointing upwards.

1. the equation of motion of the mass is
mx ̈+rx ̇ +(k1 +k2)x=k1(h−l1)+k2l2 −mg.
2. In SI units,suppose that m=8, k1 =130, k2 =70, r=40, h=2,
l1 = 0.75 and l2 = 0.75. Determine the natural angular frequency of the system to two decimal places.

BvU
Much better. Even better if you also learn a little $\TeX$ to typeset the equations:$$m\dot x + r\dot x + (k_1+k_2)x = k_1(h-l_1)+k_2l_2 - mg$$ (using the subscript buttons is intermediate ).