1. [10 Points} It is useful to visualize the motion of the boom before making measurements. You can use a simple analogy of a vertical pendulum made at home from a weight on a light string or thread about 1m long. Hold the string about waist high and wait for the motion to settle down. Now step quickly to your left about 1 foot. Wait for the pendulum to settle again, then step 2 feet to your right, wait to settie then step 1 foot to your left. a. Make a qualitative sketch of this motion ()0! plot mass position vs time). in. Next, starting from rest, try stepping leftfright in resonance with the pendulum, keeping a constant "forcing amplitude" of 1 foot. This should build asymptotically to a maximum. Note the approximate size of maximum, then stop stepping and watch the decay back to zero. Sketch this motion {KY plot position vs time]: Add a line showing your push [square wave}. c. What is the phase between your forcing step and the response? 2. [10 Points} We return now to the torsion pendulum. It is useful to consider the boom deection caused by "your body\". For this purpose, you may assume your body to be a spherical mass of ?5kg at a distance of d=1m and angle (I! from the long axis of the boom. a. Draw a force diagram for the case CD = 45 deg, with appropriate length, direction and placement of vectors. Hint: You want a "top view\". in. Explain why the net torque is 0 at angle '11) =0. Explain why the net torque is 0 at angle (13 = 90 deg. d. Consider now (I) = 45 deg. Estimate the deflection as a fraction of the \"signal" for your experiment. That is find 353.33... This is best done as a "scaling argument", considering tacit\" {rather than simply plugging in numbers for 6, etc}. e. Show that the net torque scales with distance as d3 [dipole eld]. 3. {10 pts] Theory and Correction: 5" a. Derive the result for 6 shown in Eq 4 of the handout. G =%. This result assumes a massless boom, and oniy considers the force between M and nearby mass rn, neglecting the force between M and m' {at far end of boom]. b. Show that the force between M and m' {neglected above} reduces the net torque by a fraction t,..-,.!'t,.. "' [1.06, for the parameters of this experiment. c. If you include this "correction\" in your model, does that increasefdecrease your result for G? d. Suppose you are timid in shifting the forcing mass, and you stop 1mm short of the window. By what '36 would this change your value for B? What 96 change for (3 [assuming you do not correct the input value for "5"]. Cavendish Pre-tab Exercise 1 a ( t ) ( 2 ) 1 x (t ) b. Sideways steps add constant atset I analogous to sideways force F=- GMM S C. & , Forcing stop in resonance has phare 90 from x (+ ), as required for roomant response . See "step function on phot . That "switched at TP of x ( t ): Note that phase of F (t ) matches x (t ) = 2 (t ) , so max Power ( Fault ) dt