# Differential Equation, assignment help

*label*Mathematics

*timer*Asked: Apr 29th, 2016

*account_balance_wallet*$15

**Question description**

Describe a mathematical model for swinging saloon doors from a YouTube video. The parts below provide the needed steps.

This is the Video https://www.youtube.com/watch?v=mlQkIiSLCUE&feature=youtu.be

(a) Find a suitable variable (it will depend on time) that describes the motion of one of the saloon doors.

(b) Determine the coefficients for the second order linear differential equation that describes the motion. These coefficients have to be estimated from the video.

Using the Underdamped motion.

use t = 7s

theta = pi/2

## Tutor Answer

Hello paypay:I've written up a full answer to your "Swinging Door" problem.It's attached as the following MS WORD document:Let me know any questions you may have, or any possible errors.

Solution to Swinging Door Problem

Part (a). Let θ(t) = angle of door from fully closed position (rad).

Then the differential Equation of Motion (for small values of θ) is:

(D2 +2ζnD + ωn2) θ(t) = 0

In Equation (1):

(1)

ζ = Critical Damping Ratio (---)

ωn = Undamped Natural Frequency (rad/sec)

and the differential operator D = d/dt, D2 = d2/dt2

The appropriate initial conditions to our problem, at t = 0, are:

θ = π/2 rad = 1.5708 rad

Dθ = dθ/dt = 0

It can be shown that the solution to Eq. (1), that satisfies the above

initial conditions, is:

θ(t) = (π/2)exp(-ζnt)[ cos(ndt) + {ζ/√(1-2)}sin(ndt)]

(2)

In Equation (2): nd = Damped Natural Frequency (rad/sec)

nd = ωn√(1-2)

(3)

and exp( ) stands for e( ).

Part (a). We use the YouTube video to estimate parameters ...

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