How Do You Calculate the Natural Angular Frequency of a Dual-Spring System?

[umzung]

Homework Statement

The suspension of a modified baby bouncer is modeled 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 modeled 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.

 

[BvU]

to two decimal places.

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

 

[umzung]

The full problem statement is as follows:

The suspension of a modified baby bouncer is modeled 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 modeled 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 ).

Your relevant equation applied to the undamped sytem. You want to decide if the exercise asks for the damped natural frequencey or the undamped one.

got an integer answer that requires no rounding.

In itself, that's not a problem: just quote the result as e.g. 4.00 radians/s

 

[H07715]

I have a similar question how did you find the natural angular frequency?

 

[PeroK]

I have a similar question how did you find the natural angular frequency?

It's probably best to open your own homework thread.