A designer of tennis racket is trying different stringing patterns and wants to know how they affect the peak force and the impulse of momentum $($force$-$time integral$)$ that a tennis ball transfers to the user during the contact time of less than $0\mathrm{.}1$s$.$ She has built an apparatus that can clamp the racquet rigidly in front of a ball machine that shoots tennis balls at the middle of the racket face with a precisely controlled velocity. The peak force at point of impact when shooting at a rigid wall is $10$ N$.$ The length of the racket from the middle of the face to the point on the handle where it is clamped is $0\mathrm{.}5$ m$.$ Assume that the only compliance in the racket is in its strings and make sure your measurement apparatus does not introduce significant additional compliance.

Design a cantilevered beam to hold the clamp and fit it with a pair of strain gauges that will transduce impact force at the center of the racket.

Using NI Multisim, design a bridge preamplifier that will generate an output of about $10$ V for the maximal impact force of $10$ N and describe how you would calibrate it to precisely that output.

Add an analog signal processor that will compute the impulse of momentum in which $10$V output corresponds to $1$ Ns $(10$ N x $0\mathrm{.}1$s$).$

Simulate its output waveform for a square wave representing $10$ N force lasting $0\mathrm{.}1$ s$.$

Show all calculations that inform and justify your designs.