(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The typical walking speed of a person walking at a relaxed pace can be estimated by modelling their legs as a physical pendulum. Assume that the length of a person's leg is L and it pivots about the hip and the leg is tapered (more mass towards the hip and less towards the foot). So that its rotational inertia of the leg is 1/6 MR^{2}

a) Determine the frequency of the oscillations of the leg

b) Derive a formula for the walking speed based on the frequency and the maximum angle of the oscillation

c) What is the walking speed of a person whose legs are 1m long with a center of mass at 0.45m away from the hip who is walking so the maximum angle of their legs is 30deg away from the vertical?

2. Relevant equations

a) w = sqrt (mgl / I)

Where w = oscillation frequency, m = mass, g = acc due to g, l = length, I = rotational inertia

b) v = -Aw sin(wt+theta)

where A = amplitude.

3. The attempt at a solution

From the equation at a), w = sqrt (MgL / (1/6) ML^{2})

w = sqrt (6g / L)

for b), I would have thought to use the formula as I stated in b), but since the example said to use the frequency and the maximum angle, I'm not sure which formula to use.

I thought about using the equivalent of the formula v = u + at, but I don't have the angular acceleration with me. I also briefly thought to use angular momentum to find the angular velocity before converting it to linear velocity but it seems far-fetched.

I also had thought to use a differential equation going by Torque = Ia, where I = rotational inertia and a = angular acc, and equating it to torque = mgl. Then thus, having:

MgL = 1/6 ML^2 a,

6g = aL

a = 6g/L

But I have no idea how that ties in with the question.

I suppose I have the period by playing around with w = 2pi f, turning into w = 2pi / T.

If someone could help, it will be much appreciated. Thank you :)

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# Homework Help: Walking legs as physical pendulum oscillations

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