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k x(t) 4.2. RESPONSE UNDER A GENERAL PERIODIC FORCE p(t) 50 mm diameter Chamber (a) p(t) = pressure, Pa 50,000t 50,000 (2-t) 50,000 t (sec) 0 1 τ=2 3 2τ = 4 5 (b) FIGURE 4.1 Periodic vibration of a hydraulic valve. where A is the cross-sectional area of the chamber, given by $$A = \frac{\pi(50)^2}{4} = 625 \pi mm^2 = 0.000625 \pi m^2$$ (E.2) and p(t) is the pressure acting on the valve at any instant t. Since p(t) is periodic with period τ = 2 seconds and A is a constant, F(t) is also a periodic function of period τ = 2 seconds. The frequency of the forcing function is ω = (2π/τ) = π rad/s. F(t) can be expressed in a Fourier series as $$F(t) = \frac{a_0}{2} + a_1 \cos \omega t + a_2 \cos 2\omega t + ...$$ $$+ b_1 \sin \omega t + b_2 \sin 2\omega t + ...$$ (E.3) where $a_j$ and $b_j$ are given by Eqs. (4.2) and (4.3). Since the function F(t) is given by $$F(t) = \begin{cases} 50000At & \text{for } 0 \le t \le \frac{\tau}{2} \\ 50000A(2-t) & \text{for } \frac{\tau}{2} \le t \le \tau \end{cases}$$ (E.4) the Fourier coefficients $a_j$ and $b_j$ can be computed with the help of Eqs. (4.2) and (4.3): $$a_0 = \frac{2}{\tau} \left[ \int_0^1 50000At dt + \int_1^2 50000A(2-t) dt \right] = 50000A$$ (E.5)

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Question content area top Part 1 DavidDavid and RobinRobin are married and they have two children, aged 1515 and 1919. The 1919 year old child is paralyzed and confined to a wheelchair. RobinRobin and DavidDavid pay a live-in nanny $ 25 comma 000$25,000 per year to take care of their children for the entire year. DavidDavid works full time and earns a salary of $ 123 comma 000$123,000 per year. RobinRobin works part time, earning a salary of $ 32 comma 000$32,000 per year. RobinRobin is also upgrading her education and goes to college part time during the fall semester, for a total of 1212 weeks or 33 months in the current year. Which of the following is correct with respect to DavidDavid and RobinRobin's ability to claim a deduction for child care expenses?

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A complete listing of activities required for the production of a product or service is a(n) Blank______. Multiple choice question. activity dictionary bill of activities activity cost driver

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2. You wish to have $15,000 in 5 years in a savings account with a 4\% annual interest rate, compounded monthly. How much do you need to invest now (PV) to reach your goal?

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A certain ore yields an average of 75\% iron. How much ore is needed to obtain 1,125 lb of iron? To obtain 1,125 lb of iron, \boxed{} lb of ore is needed.

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If you increase the concentration of substrates in a reaction, the reaction will Group of answer choices Its favorability will not change (\Delta G would not change) Become more favorable in the forward direction (\Delta G becomes more negative) Become less favorable in the forward direction(\Delta G becomes more positive))

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5. How could two people with albinism have a child who has normal skin pigment?

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. You have 88 mL of a bacterial cell suspension containing 8 x 10^8 cells/mL. You want to make 5 mL of a suspension from this that contains 1 x 10^5 cells/mL. How will you do this?

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Question 7 - 1 Point Using synthetic division, what is the quotient for (4x^3 + 8x^2 - 16x + 62) ÷ (x + 4)? If the remainder is non-zero, express the remainder term as a fraction using the divisor as the denominator. Provide your answer below: Quotient:

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Jayson Company projects the following sales for the first three months of the year: $12,600 in January; $12,200 in February; and $16,300 in March. The company expects 70% of the sales to be cash and the remainder on account. Sales on account are collected 50% in the month of the sale and 50% in the following month. The Accounts Receivable account has a zero balance on January 1. Round to the nearest dollar. Read the requirements. Requirement 2. Prepare a revised schedule of cash receipts if receipts from sales on account are 70% in the month of the sale, 20% in the month following the sale, and 10% in the second month following the sale. What is the balance in Accounts Receivable on March 31? (If an input field is not used, leave the input field empty. Do not enter a zero.) Cash Receipts from Customers Total sales January February March Total $ 12,600 $ 12,200 $ 16,300 $ 41,100 January February March Total Cash Receipts from Customers: Accounts Receivable balance, January 1 January-Cash sales $ 8,820 January-Credit sales, collection of January sales in January 2,646 January-Credit sales, collection of January sales in February 378 January-Credit sales, collection of January sales in March 756 February-Cash sales 8,540 February-Credit sales, collection of February sales in February February-Credit sales, collection of February sales in March 2,562 366 March-Cash sales 11,410 March-Credit sales, collection of March sales in March 3,423 Total cash receipts from customers $ 11,466 11,480 15,955 38,901

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ramon m.