# Harmonic Oscillations with Escapement [Clock]

1. Apr 28, 2012

### hkEkers

1. The problem statement, all variables and given/known data
Clock activates escapement every time it passes through the vertical. Escapment under tension from a hanging weight that gives an impulse distance l from the pivot. Energy transferred by this compensates for the energy dissipation due to friction so the amplitude is constant.

(a)What is the impulse needed to sustain the motion of a pendulum length L mass m amplitude of swing theta_0 and quality factor Q

(b) Why is it desirable for the pendulum to engage the escapement as as it passes vertical rather than another point.

2. Relevant equations

Q=(m*omega)/F_dampening
omega= sqrt(k/m)

E(t) = 1/2 A^2 [ m*omega^2*sin^2(omega*t+phi) + k*cos^2(omega*t+phi)]
E(t) = K(t) + U(t)

3. The attempt at a solution

For a, either measuring energy loss by U(x,t)= U(x,t+T) + Energy loss which I'm not sure how to solve for without it being obnoxiously long and neglecting a couple variables. No idea how to account for distance from the pivotal point in the equation without involving Torque, and considering this is a module on harmonic oscillation seems less likely.

Well for b my guess would be it's when acceleration =0 so there aren't any other forces acting on the swing at the time or so the impulse isn't applied at an angle doesn't add an acceleration to multiple axes.

I'm completely lost on how to create a relationship between a lot of the elements in this problem. Any help would be appreciated.

Last edited: Apr 28, 2012