5. The major product from the reaction shown below gave the following 1H NMR spectrum. Deduce the structure of this product and clearly assign all 1H signals. (10 pts)

Nonlinear Spring Oscillator PHY 2048C Cumulative Final Examination Points: 10 Suggested Time: 25–30 minutes Instructions: Show all work. Begin each derivation with an appropriate fundamental physics principle. Clearly define any additional symbols you introduce. Unsupported answers may not receive full credit. A cart of mass m moves without friction along a horizontal track. It is attached to a nonlinear spring whose restoring force is Fs(x) = −k0x(1 + αx) where x is measured from equilibrium, k0 > 0, and α is a constant with units of inverse length. The cart is released from rest at x = A, where 1 + αx remains positive over the entire motion. Tasks Part A. Derive the spring potential-energy function U(x), choosing U(0) = 0. Part B. Derive the speed of the cart as a function of position, v(x), while it moves from x = A toward equilibrium. Part C. Determine the cart’s speed as it passes through x = 0. Part D. Write, but do not evaluate, a definite integral that gives the time required for the cart to move from x = A to x = 0. Part E. Linearize the equation of motion for sufficiently small displacement and determine the corresponding small-amplitude angular frequency ω0. Part F. Determine the magnitude of the cart’s acceleration at the instant it is released. State how this compares with the acceleration predicted by the small-amplitude model.

An SLP explains to parents that hearing loss does not directly cause poor literacy outcomes. Which explanation BEST reflects current evidence?

During shared book reading, a parent asks, “Why do you think the boy decided to hide?” This question primarily targets:

A teacher asks how to determine whether a student with hearing loss truly understands classroom directions. Which strategy is MOST consistent with evidence-based classroom accommodations?

Which adult rehabilitation assessment would BEST support a patient-centered approach?

True or False: California entered the Union as a slave state under the Compromise of 1850. 

The formal laws used to restrict and control the lives of enslaved people were called ______________.

An 8-year-old child with bilateral cochlear implants earns mostly A’s and B’s, scores within normal limits on standardized language testing, and demonstrates excellent speech recognition in quiet. However, the teacher reports that the student rarely participates in group discussions and appears exhausted after school. Which interpretation BEST explains these findings?

A fourth-grade student with mild bilateral hearing loss is maintaining average grades but has recently begun missing classroom discussions. Which intervention BEST reflects the philosophy of indirect services?